Download Impurity transport modelling in the scrape off layer - DORAS

Impurity transport modelling in the scrape off layer of
the MAST tokamak using DIVIMP-OSM-EIRENE
and carbon injection
Mr. Huw Jonathan Leggate
A dissertation submitted in fulfilment of the
requirements for the award of
Doctor of Philosophy (Ph.D.)
presented to the
School of Physical Science
Faculty of Science and Health
Dublin City University
Supervisor: Prof. Miles M. Turner
December, 2015
Declaration
I hereby certify that this material, which I now submit for assessment on the
programme of study leading to the award of Doctor of Philosophy is entirely
my own work, that I have exercised reasonable care to ensure that the work
is original, and does not to the best of my knowledge breach any law of
copyright, and has not been taken from the work of others save and to the
extent that such work has been cited and acknowledged within the text of
my work.
Signed .....................................................
Huw Jonathan Leggate
Student ID: 58116192
Date: December 21, 2015
i
Contents
Table of Contents
ii
Acknowledgements
vii
Publications
ix
List of Figures
x
List of Tables
xxi
Abstract
xxii
1 Introduction
1.1
1
Edge plasma transport . . . . . . . . . . . . . . . . . . . . . .
2
1.1.1
Parallel and perpendicular transport . . . . . . . . . .
2
1.1.2
Radial asymmetry . . . . . . . . . . . . . . . . . . . .
4
1.1.3
Particle drifts . . . . . . . . . . . . . . . . . . . . . . .
5
1.1.4
Flow reversal . . . . . . . . . . . . . . . . . . . . . . .
8
ii
CONTENTS
1.1.5
1.2
1.3
1.4
1.5
Turbulence . . . . . . . . . . . . . . . . . . . . . . . .
8
Impurities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.1
The effect of impurities on the plasma . . . . . . . . . 10
1.2.2
Impurity generation . . . . . . . . . . . . . . . . . . . . 11
1.2.3
Impurity transport . . . . . . . . . . . . . . . . . . . . 12
Plasma boundary diagnostics and experimental techniques . . 14
1.3.1
Principle plasma boundary diagnostics . . . . . . . . . 14
1.3.2
Impurity injection experiments . . . . . . . . . . . . . 18
Modelling Impurities in the Scrape-Off Layer . . . . . . . . . . 23
1.4.1
Approaches to Impurity Modelling . . . . . . . . . . . 23
1.4.2
The Two-Point Model . . . . . . . . . . . . . . . . . . 23
1.4.3
1D fluid modelling along B
1.4.4
Modelling the SOL in 2 dimensions . . . . . . . . . . . 28
1.4.5
The Onion Skin Method . . . . . . . . . . . . . . . . . 30
1.4.6
Further SOL modelling . . . . . . . . . . . . . . . . . . 32
1.4.7
Kinetic impurity models . . . . . . . . . . . . . . . . . 33
. . . . . . . . . . . . . . . 25
The MAST tokamak . . . . . . . . . . . . . . . . . . . . . . . 35
2 Carbon injector design and testing
37
2.1
Design motivation . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2
The injector design . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1
2.3
2.4
The spark head . . . . . . . . . . . . . . . . . . . . . . 38
Injector development . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.1
Test conditions . . . . . . . . . . . . . . . . . . . . . . 39
2.3.2
Observed pressure increase . . . . . . . . . . . . . . . . 40
2.3.3
Ablated mass measurements . . . . . . . . . . . . . . . 43
2.3.4
Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Final design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
iii
CONTENTS
2.5
2.4.1
The injector head . . . . . . . . . . . . . . . . . . . . . 47
2.4.2
Power supplies and triggering . . . . . . . . . . . . . . 50
2.4.3
Modification after initial commissioning . . . . . . . . . 51
Installation on MAST . . . . . . . . . . . . . . . . . . . . . . 51
3 Experimental method and data
3.1
3.2
Experimental approach . . . . . . . . . . . . . . . . . . . . . . 60
3.1.1
First use . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.1.2
Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . 61
Experimental data . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2.1
Plasma configuration . . . . . . . . . . . . . . . . . . . 64
3.2.2
Injection duration . . . . . . . . . . . . . . . . . . . . . 66
3.2.3
Injection location . . . . . . . . . . . . . . . . . . . . . 68
3.2.4
Electron temperature and density data . . . . . . . . . 74
3.2.5
Flow data . . . . . . . . . . . . . . . . . . . . . . . . . 79
4 Image processing and analysis
4.1
Camera Calibration . . . . . . . . . . . . . . . . . . . . 84
Magnetic field projection . . . . . . . . . . . . . . . . . . . . . 84
4.2.1
4.3
82
Acquired CCD data . . . . . . . . . . . . . . . . . . . . . . . . 82
4.1.1
4.2
60
Camera registration and field line projection . . . . . . 84
Image processing . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.3.1
CII emission . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3.2
CI and CIII emission . . . . . . . . . . . . . . . . . . . 88
4.4
Emission parallel to the magnetic field . . . . . . . . . . . . . 95
4.5
Repeat injection . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 DIVIMP Simulation
5.1
106
OSM-EIRENE-DIVIMP . . . . . . . . . . . . . . . . . . . . . 106
iv
CONTENTS
5.2
5.3
5.1.1
OSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.1.2
EIRENE . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.1.3
DIVIMP . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Plasma solution . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.2.1
Simulation Equilibrium . . . . . . . . . . . . . . . . . . 110
5.2.2
Background plasma simulation . . . . . . . . . . . . . . 112
5.2.3
Flow comparisons . . . . . . . . . . . . . . . . . . . . . 115
Simulated impurity injection initial conditions . . . . . . . . . 116
5.3.1
Initial radial position of injected impurity . . . . . . . 117
5.3.2
Initial Z position . . . . . . . . . . . . . . . . . . . . . 117
5.3.3
Injection duration . . . . . . . . . . . . . . . . . . . . . 118
5.3.4
Initial energy distribution . . . . . . . . . . . . . . . . 118
5.3.5
Number of injected ions . . . . . . . . . . . . . . . . . 120
5.4
Parallel transport simulations for comparison with experiment 121
5.5
Comparison between experiment and simulation . . . . . . . . 121
5.6
5.5.1
Lack of observed CIII emission . . . . . . . . . . . . . 122
5.5.2
Effect of radial location on emission . . . . . . . . . . . 123
5.5.3
Relative contribution of the transport mechanisms . . . 123
Role of drift terms in simulation results . . . . . . . . . . . . . 124
5.6.1
Effect of drift terms on background plasma solution . . 125
5.6.2
Direct impact of drift terms on plume evolution . . . . 126
6 Conclusions and further work
6.1
6.2
146
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.1.1
Injection system . . . . . . . . . . . . . . . . . . . . . . 146
6.1.2
Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 147
Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
v
CONTENTS
Bibliography
152
Appendices
178
A Manufacturing drawings of the injector head
178
B Electrical schematics of the MAST installation
194
C Commissioning and initial experiments
200
C.1 Commissioning and in-situ testing . . . . . . . . . . . . . . . . 200
C.2 First experimental sessions - Oct 2011
. . . . . . . . . . . . . 201
C.2.1 Wednesday 5th October 2011 . . . . . . . . . . . . . . . 202
C.2.2 Friday 7th October 2011 . . . . . . . . . . . . . . . . . 202
C.2.3 Friday 14th October 2011 . . . . . . . . . . . . . . . . . 203
C.2.4 Monday 17th October 2011 . . . . . . . . . . . . . . . . 203
vi
Acknowledgements
I would first like to thank my Supervisor Miles Turner for his long lasting support and trust, in particular in allowing me to explore my experimental side
in the early stages of this work, also my thanks go to my co-supervisor Steven
Lisgo for providing both ideas and knowledge. I would also like to thank the
support staff in the National Centre for Plasma Science and Technology, in
particular Samantha Fahy, Sarah Hayes and Sheila Boughton, without whom
very little of this work would have been possible.
Several past members of the NCPST also helped me during this time,
James Lawlor, Niall O’Connor and Dave O’Farrell, who successfully prevented me from electrocuting myself in the lab and also shared a mutual
appreciation of beer. Also in the laboratory, Pat Wogan, Nishant Sirse, Gurusharan Singh Gogna and Mubarak Mujawar for providing guidance. Shantanu Karkari for asking awkward questions and Sarveshwar Sharma also for
asking awkward questions as well as a constant smiling presence and many
knowledgeable discussions on cricket. I would also like to mention more re-
vii
Acknowledgements
cent colleagues at DCU, Nina Hanzlikova, Sean Kelly and Samir Kechkar for
their help and occasional heated discussions.
I would not have completed this work without the generous support of all
those at the Culham Science Centre, in particular James Harrison, Andrew
Thornton, Andrew Kirk, Geoff Fishpool, Scott Allan, Sarah Elmore, Scott
Silburn, Robert Stephen, Ian Fitzgerald, Brian Lloyd and William Morris,
apologies for those I have missed off this list.
I would like to express my thanks and love to my dear friend David
Norland, who is not here to see the completion of this work but throughout
my life always kept me honest and truthful.
The support of my wife Claire McKenna has been invaluable and I will
be ever grateful for her ability to remain fun and loving under enormous
pressure.
I would like to thank Father Christmas for making Cian smile.
My greatest thanks go to my Mother and Father, Gaynor and Peter, who
have put up with considerably more than should have been and are still most
wonderfully loving and supportive.
This work was part-funded by the RCUK Energy Programme [under
grant EP/I501045] and by the European Communities. To obtain further
information on the data and models underlying this paper please contact
[email protected]. The views and opinions expressed herein
do not necessarily reflect those of the European Commission or the ITER
Organisation.
viii
Publications
• Divertor impurity injection using high voltage arcs for impurity transport studies on the Mega Amp Spherical Tokamak, H. J. Leggate, S.
W. Lisgo, J. R. Harrison, S. Elmore, S. Y. Allan, R. C. Gaffka, R.
C. Stephen and M. M. Turner, Review of Scientific Instruments, 85,
123503 (2014);http://dx.doi.org/10.1063/1.4903352
• Carbon injection into MAST L-mode and H-mode plasmas as an indicator of impurity transport, H. J. Leggate, J.R. Harrison, S.A. Silburn
and M.M. Turner, 41st EPS Conference on Plasma, Berlin, Germany,
23-27 June, 2014
• Impurity transport studies using fast imaging of injected carbon on the
MAST tokamak, H. J. Leggate, S. W. Lisgo, J. R. Harrison, S. Elmore,
S. Y. Allan and M. M. Turner, 39th EPS Conference on Plasma Physics,
Stockholm, Sweden, 2-6 July, 2012
ix
List of Figures
1.1
The temperature gradient force drives impurities up the temperature gradient. Ions and electrons impacting the impurity
ion Z from the lower temperature side will have lower average
temperatures and collision frequency than ions and electrons
from the hotter side. They will therefore transfer less momentum to the impurity ion resulting in a net force F in the
direction of increasing temperature. . . . . . . . . . . . . . . . 14
1.2
A typical onion skin geometry in the poloidal plane from a
MAST plasma with the MAST first wall also plotted . . . . . 31
2.1
Possible electrode geometries . . . . . . . . . . . . . . . . . . . 41
2.2
Conceptual design for the carbon injector . . . . . . . . . . . . 41
2.3
Developmental injector head . . . . . . . . . . . . . . . . . . . 41
2.4
Discharge pressure increase . . . . . . . . . . . . . . . . . . . . 42
2.5
Quartz monitor crystal probe . . . . . . . . . . . . . . . . . . 46
x
LIST OF FIGURES
2.6
Fast visible images of the plume . . . . . . . . . . . . . . . . . 46
2.7
Discharge current pules . . . . . . . . . . . . . . . . . . . . . . 48
2.8
EDX spectrograms of ablated material . . . . . . . . . . . . . 48
2.9
SEM image of the ablated material . . . . . . . . . . . . . . . 53
2.10 Close up of the injector head . . . . . . . . . . . . . . . . . . . 54
2.11 Exploded view of the injector head . . . . . . . . . . . . . . . 55
2.12 Cutaway of the assembled head . . . . . . . . . . . . . . . . . 56
2.13 Image of the injector head prior to installation on MAST . . . 56
2.14 Cutaway showing integrated Langmuir probe . . . . . . . . . . 57
2.15 Schematic of the divertor science facility . . . . . . . . . . . . 58
2.16 Cutaway of a dummy injector head in position . . . . . . . . . 59
2.17 Schematic of the the installed injector head seen from above . 59
3.1
View from the sector one fast camera . . . . . . . . . . . . . . 63
3.2
View from the sector 11 fast camera . . . . . . . . . . . . . . . 63
3.3
Dα emission, plasma current, neutral beam total injected power,
line integrated density and toroidal magnetic field on the magnetic axis for the L-mode shots 29125, 29126, 29128 and 29129.
The impurity injection times are denoted by dashed vertical
black lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4
Dα emission, plasma current, neutral beam total injected power,
line integrated density and toroidal magnetic field on the magnetic axis for the H-mode shots 29139 and 29142. The impurity injection time is denoted by a dashed vertical black line. . 67
3.5
Injector discharge current measure by the integrated current
transformer. The solid lines show the current from the first
shot in each plot while the dashed line the second. . . . . . . . 69
xi
LIST OF FIGURES
3.6
Maximum carbon II emission observed within 5 pixels of the
injection location for the three shots 29125, 29126 and 29139.
This provides an estimate of the duration of carbon injection
of approximately 40µs for the L-mode cases and 60µs for the
H-mode case. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.7
EFIT and LP data from shot 29125 showing the strike point
position at the injection time of 250ms. a) Strike point location plotted against time shows the strike point moving outwards until it crosses the injector head then moves inwards
again. b) Radial density profile from the divertor Langmuir
probes, the strike point lies close to the peak of this profile.
c) Saturation current from the on-board Langmuir probe plotted against time showing an increase just before the injections
time as the strike point crosses the injector. . . . . . . . . . . 71
3.8
EFIT and LP data from shot 29126 showing the strike point
position at the injection time of 240ms. a) Strike point location plotted against time shows the strike point moving outwards until it crosses the injector head then moves inwards
again. b) Radial density profile from the divertor Langmuir
probes, the strike point lies close to the peak of this profile.
c) Saturation current from the on-board Langmuir probe plotted against time showing an increase just before the injections
time as the strike point crosses the injector. . . . . . . . . . . 72
xii
LIST OF FIGURES
3.9
EFIT and LP data from shot 29139 showing the strike point
position at the injection time of 320ms. a) Strike point location plotted against time shows the strike point moving outwards until it crosses the injector head then moves inwards
again. b) Radial density profile from the divertor Langmuir
probes, the strike point lies close to the peak of this profile.
c) Saturation current from the on-board Langmuir probe plotted against time showing an increase just before the injections
time as the strike point crosses the injector. . . . . . . . . . . 73
3.10 Saturation current plotted against time taken from the onboard Langmuir probe. There is no discernible perturbation
seen at the injection time for each shot, shown by a dashed
vertical line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.11 Outer target electron density and temperature data against
normalised poloidal flux for L-mode shot 29125. The measured
data is represented by crosses and the data used in simulation
by the solid line. . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.12 Outer target electron density and temperature data against
normalised poloidal flux for L-mode shot 29126.The measured
data is represented by crosses and the data used in simulation
by the solid line. . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.13 Outer target electron density and temperature data against
normalised poloidal flux for H-mode shot 29139. The measured data is represented by crosses and the data used in simulation by the solid line. . . . . . . . . . . . . . . . . . . . . . 78
xiii
LIST OF FIGURES
3.14 Midplane electron density and temperature data for shot 29125
and 29139 against normalised poloidal flux. Data from the
high and low field sides have been combined. . . . . . . . . . . 80
3.15 Flow data taken using the coherence imaging diagnostic measuring carbon III emission [1]. . . . . . . . . . . . . . . . . . . 81
4.1
Unfiltered images from both sectors showing the actual camera
views. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2
Unprocessed images from both sectors showing CII filtered images from shot 27075. Injection location 4cm into the private
flux zone with an integration time of 33µs. . . . . . . . . . . . 83
4.3
Calibration curves for the carbon II, carbon III and Dα filters.
4.4
Contour plots of the carbon plumes from L-mode pulse 29125
85
imaged from sector 1 using a CII filter at 515nm. The images
are each separated by 13µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 89
4.5
Contour plots of the carbon plumes from L-mode pulse 29125
imaged from sector 11 using a CII filter at 515nm. The images
are each separated by 13µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 90
4.6
Contour plots of the carbon plumes from L-mode pulse 29126
imaged from sector 1 using a CII filter at 515nm. The images
are each separated by 13µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 91
4.7
Contour plots of the carbon plumes from L-mode pulse 29126
imaged from sector 11 using a CII filter at 515nm. The images
are each separated by 10µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 92
xiv
LIST OF FIGURES
4.8
Contour plots of the carbon plumes from H-mode pulse 29139
imaged from sector 1 using a CII filter at 515nm. The images
are each separated by 13µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 93
4.9
Contour plots of the carbon plumes from H-mode pulse 29139
imaged from sector 11 using a CII filter at 515nm. The images
are each separated by 10µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 94
4.10 Contour plots of the carbon plumes from L-mode pulse 29128
imaged from sector 1 using a CI filter at 910nm. The images
are each separated by 13µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 95
4.11 Contour plots of the carbon plumes from L-mode pulse 29128
imaged from sector 11 using a CIII filter at 465nm. The images
are each separated by 10µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 96
4.12 Contour plots of the carbon plumes from L-mode pulse 29129
imaged from sector 1 using a CI filter at 910nm. The images
are each separated by 13µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 97
4.13 Contour plots of the carbon plumes from L-mode pulse 29129
imaged from sector 11 using a CIII filter at 465nm. The images
are each separated by 10µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 98
xv
LIST OF FIGURES
4.14 Contour plots of the carbon plumes from H-mode pulse 29142
imaged from sector 1 using a CI filter at 910nm. The images
are each separated by 13µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 99
4.15 Contour plots of the carbon plumes from H-mode pulse 29142
imaged from sector 11 using a CIII filter at 465nm. The images
are each separated by 10µs. Magnetic field lines originating
at the injection radius can be seen projected onto the image. . 100
4.16 CII emission intensity along the field line from sectors 1 (a)
and 11 (b) for shot 29125 . . . . . . . . . . . . . . . . . . . . . 102
4.17 CII emission intensity along the field line from sectors 1 (a)
and 11 (b) for shot 29126 . . . . . . . . . . . . . . . . . . . . . 103
4.18 CII emission intensity along the field line from sectors 1 (a)
and 11 (b) for shot 29139 . . . . . . . . . . . . . . . . . . . . . 104
4.19 Secondary injection. CII filtered images taken from shot 29126
(a) and shot 29139 (b) showing the initial injection in the
first frame and a secondary burst of carbon in frames 7 and 5
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.1
Grids used for the impurity injection simulation. These are
produced using EFIT magnetic equilibrium reconstruction. . . 111
5.2
Background plasma simulation for shot 29125 . . . . . . . . . 113
5.3
Background plasma simulation for shot 29126 . . . . . . . . . 114
5.4
Background plasma simulation for shot 29139 . . . . . . . . . 114
xvi
LIST OF FIGURES
5.5
Sensitivity scan using background plasma solutions with the
target or midplane data shifted by ψn ± 0.01. Each plot shows
simulated carbon II and carbon III emission parallel to the
magnetic field from the injection location. s is the parallel
distance along the flux tube. . . . . . . . . . . . . . . . . . . . 128
5.6
Sensitivity scan using background plasma solutions with the
target or midplane data shifted by ψn ± 0.02. Each plot shows
simulated carbon II and carbon III emission parallel to the
magnetic field from the injection location. s is the parallel
distance along the flux tube. . . . . . . . . . . . . . . . . . . . 129
5.7
Density along the magnetic field for the simulation tube where
the injection takes place. . . . . . . . . . . . . . . . . . . . . . 130
5.8
Density along the magnetic field for simulation tubes just outside the strike points for shots 29125 and 29126. The data for
tube 13 can be taken as identical as expected, there is however
a difference in the gradient for tube 12, which is closer to the
strikepoint. This is due to differences in the midplane data,
and is small enough to be unlikely to have a significant effect
on the impurity simulations. . . . . . . . . . . . . . . . . . . . 131
5.9
Comparison of measured and simulated parallel flow using the
coherence imaging diagnostic and carbon III emission lines,
see section 1.3.1. . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.10 Comparison of transport parallel to the magnetic field for
CII and CIII ions injected at 0.1eV, 1eV , 10eV and 100eV
at 10µs, 20µs, 30µs and 40µs after injection for shot 29125. s
is the distance along the magnetic field from the lower target. 133
xvii
LIST OF FIGURES
5.11 Comparison of transport parallel to the magnetic field for
CII and CIII ions injected at 0.1eV, 1eV , 10eV and 100eV
at 10µs, 20µs, 30µs and 40µs after injection for shot 29126. s
is the distance along the magnetic field from the lower target. 134
5.12 Comparison of transport parallel to the magnetic field for
CII and CIII ions injected at 0.1eV, 1eV , 10eV and 100eV
at 10µs, 20µs, 30µs and 40µs after injection for shot 29139. s
is the distance along the magnetic field from the lower target. 135
5.13 Comparison of transport parallel to the magnetic field for CII
(a) and CIII (b) ions injected into shot 29125. Each frame
shows emission along a different flux tube starting at radial
locations 0.986m, 0.995m and 1.016m. s is the distance along
the magnetic field from the lower target. . . . . . . . . . . . . 136
5.14 Comparison of transport parallel to the magnetic field for CII
(a) and CIII (b) ions injected into shot 29126. Each frame
shows emission along a different flux tube starting at radial
locations 0.975m, 0.982m and 0.990m. s is the distance along
the magnetic field from the lower target. . . . . . . . . . . . . 137
5.15 Comparison of transport parallel to the magnetic field for CII
(a) and CIII (b) ions injected into shot 29139. Each frame
shows emission along a different flux tube starting at radial
locations 0.983m, 0.993m and 1.00m. s is the distance along
the magnetic field from the lower target. . . . . . . . . . . . . 138
5.16 Comparison with experiment of transport parallel to the magnetic field for CII ions for L-mode shot 29125. s is the distance
along the magnetic field from the lower target. . . . . . . . . . 139
xviii
LIST OF FIGURES
5.17 Comparison with experiment of transport parallel to the magnetic field for CII ions for L-mode shot 29126. s is the distance
along the magnetic field from the lower target. . . . . . . . . . 140
5.18 Comparison with experiment of transport parallel to the magnetic field for CII ions for H-mode shot 29139. s is the distance
along the magnetic field from the lower target. . . . . . . . . . 141
5.19 Comparison with experiment of transport parallel to the magnetic field for CII ions for L-mode shot 29125. s is the distance
along the magnetic field from the lower target. . . . . . . . . . 142
5.20 Comparison with experiment of transport parallel to the magnetic field for CII ions for H-mode shot 29139 with (a) 1cm
and and (b) 2cm shift applied to the injection location. s is
the distance along the magnetic field from the lower target.
. 143
5.21 Simulations with terms affecting impurity transport suppressed
for shots 29125, 29126 ad 29139. The legend indicates the
force term that has been suppressed. In each case the left
panel shows the suppression of forces due to the temperature
gradient, friction and electric field, these do not have a significant effect on the result. The middle panel shows simulations
run without collisions and with the cross-field diffusion set to
0m2 s−1 . The right panel shows impurities injected with energy of 0eV , this appears to be the most significant factor in
determining transport. s is the distance along the magnetic
field from the lower target. . . . . . . . . . . . . . . . . . . . . 144
xix
LIST OF FIGURES
5.22 Approximate direction of the radial and poloidal drifts in the
image plane for for sectors 1(a) and 11(b) for H-mode shot
29139 40µs after injection. The plume appears to drift poloidally
away from the magnetic field with the effect being more pronounced in the sector 11 image. Care must be taken in the
interpretation of this due to errors in the magnetic equilibrium
and magnetic field projection. . . . . . . . . . . . . . . . . . . 145
xx
List of Tables
3.1
Shots from the final experimental session
4.1
Camera registration . . . . . . . . . . . . . . . . . . . . . . . . 86
xxi
. . . . . . . . . . . 65
Abstract
Impurity transport modelling in the scrape off layer of the MAST
tokamak using DIVIMP-OSM-EIRENE and carbon injection
Mr. Huw Jonathan Leggate
Non-hydrogenic impurities play a significant role in the performance of magnetically confined fusion devices, causing increased radiation and dilution of
the Deuterium-Tritium fuel isotopes. Impurities are generated at the plasma
wall interfaces as well as being deliberately introduced into the plasma in
order to reduce heat loads to the vessel walls. The quantity of impurities
reaching the core plasma is determined by the impurity source and the nature
of transport in the plasma core and scrape-off layer. Direct measurements of
impurity transport have been made by injecting carbon ions into the MAST
tokamak using an electrical discharge between 2 carbon electrodes. The emission of the resultant carbon plumes was measured by 2 cameras operating at
75kHz − 100kHz mounted on the MAST vessel. The resultant transport of
the carbon ions parallel to the background magnetic field was then compared
against simulation using the DIVIMP-OSM-EIRENE code.
xxii
CHAPTER
1
Introduction
An understanding of transport phenomena in the Scrape-Off Layer (SOL) of
tokamak plasmas is of key importance in the development of next generation fusion devices such as ITER [2]. Both the control of the heat load on
plasma facing components and the control of impurities including helium ash
removal are critically dependent on SOL transport. An improved understanding of the processes in the SOL may also provide insight into other plasma
processes associated with the plasma boundary such as the edge transport
barrier present in H-mode discharges. It is useful at this point to make a distinction between the plasma edge and the SOL, the former covers not only
the region outside the Last Closed Flux Surface (LCFS) of the plasma but
extends a short distance inwards from the LCFS, covering the H-mode edge
transport barrier and associated complex atomic physics. The SOL, although
included in the term edge plasma, stops at the last closed flux surface. This
1
1.1 Edge plasma transport
thesis deals only with SOL physics and will use the terms SOL and plasma
boundary interchangeably.
Over the first few decades of fusion research little attention was paid to
the plasma boundary. However, the introduction of the diverted tokamak
[3] and the discovery of the H-mode [4] focused attention on the problems
of impurity transport into the core plasma via the SOL and on the higher
levels of power loading on the small plasma wetted areas of the first wall.
Since then the resources directed to diagnosing and modelling the plasma
boundary have increased significantly. Much of the early results of this work
are documented in a book written by Peter Stangeby, The Plasma Boundary
of Magnetic Fusion Devices[5], which also explores the foundations of the
physics of the plasma boundary. Since this publication, efforts towards an
improved understanding have continued and a large body of work on the
edge of tokamak plasmas now exists. This thesis aims to add to this work
through an understanding of the transport of impurities in the tokamak divertor and here briefly describes the mechanisms affecting this as well as the
experimental and computational methods commonly used.
1.1
1.1.1
Edge plasma transport
Parallel and perpendicular transport
The transport of impurities is naturally dependant on the hydrogenic background plasma itself and the transport processes operating within it. In
general plasma transport parallel to the local magnetic field is orders of magnitude greater than transport perpendicular to the field lines. This makes it
useful to treat parallel transport independently from other directions of transport. Parallel flows exist in the SOL, primarily driven by particle sources
2
1.1 Edge plasma transport
arising from the ionisation of neutrals from the targets and main chamber
wall, by cross field diffusion across the separatrix from the bulk plasma and
particle sinks present at the targets. These sources and sinks create variations in the plasma pressure along the SOL resulting in pressure gradient
dp
forces − n1 dx
that drive flows in the SOL. The large source at the separatrix
mean that these flows are often, though not always directed along the magnetic field towards the divertor targets. The fluid is transported along field
lines with a velocity of the order the plasma sound speed cs where[5]
r
cs = [(γe ZkTe + γi kTi )/mi ]
1/2
≈
2kTe
mi
(1.1)
where Te and Ti are the electron and ion temperatures, mi is the ion
mass and γe and γi are the adiabatic indices of the electrons and ions. For
typical SOL temperatures in the range 1-100 keV and assuming Te = Ti , the
sound speed is of order 104 − 105 ms−1 . The SOL length L ≈ πRq is typically
∼ 50m, giving a typical dwell time in the SOL of τSOL ≈ 1ms. This estimate
of the SOL dwell time relies on ∇T = 0, which in a tokamak plasma is not
the case. This approximation of an isothermal SOL is one feature of what
is known as the simple SOL, when temperature gradients are included the
SOL is referred to as complex.
Cross-field plasma velocities v⊥ are often orders of magnitude less than
the fast parallel flow vk , so that the SOL width is very small. If one makes
the assumption that cross-field transport is diffusive [6],
v⊥ ≈ D⊥ /l⊥
(1.2)
where l⊥ is the characteristic density scale length and D⊥ is the cross-field
diffusion coefficient, then the SOL width is given by
3
1.1 Edge plasma transport
λSOL
D⊥ L
≈
cs
1/2
(1.3)
However, diffusivities calculated from first principles lead to SOL widths
that are considerably less than those observed experimentally[7, 8]. This
leads to the conclusion that cross field diffusion is not sufficient to account
for cross-field transport in the SOL, and other mechanisms such as particle
drifts and turbulence are likely to play a significant role.
1.1.2
Radial asymmetry
From early on in tokamak development it was observed that strong asymmetries existed in temperature, density and power measurements measurements between the inner and outer targets of divertor discharges [9] [10]
[11]. Temperature and power are seen to be significantly higher on the outboard divertor, while plasma density is higher on the inboard divertor. These
asymmetries can be largely explained due to the geometric configuration of
tokamaks. Firstly the outboard surface area of a tokamak discharge is several
times larger than the inboard surface area, leading to an increased power flux
across the separatrix into the outboard SOL assuming uniform power flow
density over the SOL. A second effect is that of flux compression on the outboard side due to Shafranov shift, which increases the power density to the
outboard SOL and hence outboard divertor target based on the assumption
that cross field transport is dependent on spatial gradients.
The observed asymmetry is highly dependent on the plasma configuration. Double null configuration experiments on the PDX tokamak have shown
a ratio in deposited energy between the inner and outer divertor targets of
∼ 9[9]. Single null configurations typically showed much less asymmetry[12],
closer to a ratio of 2. This difference can be heuristically explained by the
4
1.1 Edge plasma transport
connection between the inner and outer SOL for single null discharges, the
fast parallel transport acts to equalise temperature and density across the
SOL.
Although the in/out asymmetries can be partially explained by geometric
considerations continued research showed that the asymmetries also depend
on the direction of the toroidal magnetic field BT [13][14] and on the discharge
density[15], with the asymmetries increasing as density increases until both
divertor targets enter the detached regime when the asymmetries all but
disappear.
1.1.3
Particle drifts
When searching for mechanisms to drive the change in asymmetry with the
direction of magnetic field it is natural to look for forces acting on the plasma
fluid that are themselves dependent on the magnetic field. The toroidal
plasma current present in tokamak plasmas is driven by the toroidal electric
field Eφ created by the transformer action of the central solenoid. This field
causes ions in the SOL to drift towards the inner or outer targets depending
on the direction of BT . The direction of BT is best defined using the direction
of the induced B × ∇B drift[6],
v∇B = ±
2
v⊥
m
B × ∇B
2eB 3
(1.4)
where v⊥ is the gyroscopic speed and m is the mass of the species. This
drift is vertical and for the direction of ’normal’ clockwise BT is downwards
towards the targets for ions and upwards for electrons. For ∇B drift towards
the targets the Eφ ion drift is directed towards the inner target, independent
of the direction of plasma current[5].
5
1.1 Edge plasma transport
Aside from the toroidally induced drifts, the electric fields present in the
SOL also affect particle transport in the form of E × B drifts [16]
vE×B =
E×B
B2
(1.5)
Electric fields exist throughout the SOL, affecting both parallel and perpendicular transport. Radial electric fields due to the temperature gradient
across the SOL cause poloidal drifts and the poloidal electric fields along the
SOL cause radial drifts, strong fields close to the targets due to the plasma
sheath also cause radial drifts. It should be noted that the drifts do not
depend on the sign of the electric charge, so electrons and ions are affected
in the same way and no charge separation occurs.
The poloidal Er × B drift acts in the same direction as the standard parallel flow seen in the SOL, for B × ∇B downwards the drifts tend to increase
density at the outer target and decrease density at the inner. This pressure
imbalance should then result in plasma flow from the outer to inner divertor.
Radial Eθ × B particle drifts cause a particle flux across the separatrix, for
B × ∇B downwards the flux is from the SOL into the main plasma on the
outer SOL and from the main plasma into the SOL on the inboard side. In
the simplest case this flux creates a source at the inboard SOL which then
drives plasma flow from the inner to outer targets. One would then expect
an increase in density at the inner target and a drop in target temperature.
Pressure gradient induced drifts are also present in the SOL, known as
diamagnetic drifts
v∇p =
B × ∇p
enB 2
(1.6)
These drifts are divergence free and therefore do not result in net plasma
flow to the divertor targets [17]. However v∇p is dependent on the sign of
6
1.1 Edge plasma transport
the charge and so ion and electron drifts are in opposite directions, leading
to currents in the SOL.
Drifts in the SOL can also contribute to the parallel flow. The ∇B
drift(1.4) causes ions and electrons to drift vertically in opposite directions.
The curvature drift[6]
vcurv = ±
vk2 m
eB 3
B × ∇B
(1.7)
due to the curvature of the magnetic field lines acts in the same direction
and these two drifts result in vertical charge separation. This then drives
parallel currents in the SOL that contribute to parallel flow in the SOL,
known as Pfirsch-Schluter (P-S) flow. Poloidal Er × B drift also contributes
to the P-S flow directly, though does not contribute to the Pfirsch-Schluter
currents as the drift direction is independent of species charge. An important
prediction of P-S flow is that the flow velocity will be at a maximum at the
outer midplane and a negative minimum at the inner midplane, changing
with field direction.
The drifts present in the SOL play a significant role, a simple example
illustrates this, estimating the poloidal E × B drift velocity as[5],
vE×B ≈
3kTe
eλTe B
(1.8)
where λTe = 10−2 m is the electron temperature decay length, Te = 25eV
and B = 3T gives vE×B ≈ 2500ms−1 . A typical magnetic pitch angle of 10
degrees gives a poloidal projection of the sound speed estimated previously
(1.1) of approximately 2000ms − 20000ms, so in this example the drift velocity is at the lower end of the range of sound speeds and would be likely
to have an observable effect on the SOL.
7
1.1 Edge plasma transport
1.1.4
Flow reversal
One might expect parallel plasma flow in the SOL to be towards the targets
at all points, taking particles that have diffused across the separatrix towards
the targets. However, it has been shown [18] that under certain conditions
the plasma flow can reverse close to the separatrix. This has been verified
experimentally [19] [20] though the exact mechanisms governing this effect are
not fully understood. One basic explanation [5] is that of radial temperature
gradients across the SOL that allow neutrals from the walls of the divertor
to cross the outer (cooler) part of the SOL and become ionised close to the
separatrix upstream from the target, introducing a particle source potentially
greater than the sink available at the target. Particle balance is satisfied by
flow away from this over dense region towards the main plasma. However,
observations have shown that flow-reversal can be instigated by reversing the
toroidal magnetic field [21] [20] implying that BT dependent plasma drifts and
associated flows also play a role. Flow-reversal is of particular importance
as it can allow the transport of impurities from the targets in to the main
plasma, which is problematic for future reactor design, see 1.2.1.
1.1.5
Turbulence
In recent work on asymmetries, flow reversal and plasma transport has
started to include turbulence as a significant and potentially dominant process[8,
22]. It has long been recognised that turbulence was likely to play a major
role in tokamak plasmas but it is only recently that high speed diagnostics and High Performance Computing (HPC) environments have allowed
the subject to be more fully explored. Though the effect of turbulence on
plasma transport is far from fully understood it is clear that it plays a ma-
8
1.1 Edge plasma transport
jor role in cross-field transport [23]. The first indication that a turbulent
explanation was required was the large SOL widths observed in experiment,
considerably greater than that expected due to purely diffusive transport[24],
1.3.
Turbulent transport in the plasma core has been shown to have the characteristics of drift-Alfvén turbulence[25, 26]. Edge turbulence is less easy to
characterise, though it appears to be dominated by large cross-field transport events known as ’blobs’ [23]. The turbulent transport of these blobs
has been suggested to be interchange-mode-like in character[27] while another approach[28] suggests radial advection of the blob structures. Detailed
investigation of the edge turbulence has shown that the fluctuations are intermittent and strongly non-Gaussian with the probability distribution function
of density fluctuations being asymmetric and having tails that are consistent
with exponential decay of probability with fluctuation amplitude[29, 30]. It
is also important to note the large range of length scales associated with the
turbulent fluctuations[31]. These structures have been observed experimentally [32, 33] and understanding their dynamics is key to understanding SOL
transport.
The effect of turbulent fluctuations on parallel flow is poorly understood.
It is likely that the convective cells caused by plasma blobs generate sheared
zonal flows[34], however sheared flows tend to suppress turbulence [35], so
that parallel flows and turbulence are likely to be strongly coupled. Turbulence may also play a strong role in flow asymmetries, for double null
discharges parallel flow at the mid-plane inner SOL is much weaker than
flows in the outer SOL, while for single null discharges the difference is much
less pronounced. It has been suggested that poloidal gradients caused by
ballooning induced turbulence in the outer SOL drive flows that in single
9
1.2 Impurities
null discharges also affect the inner SOL[36]. For double-null discharges the
inner SOL particle flux has been measured to be considerably lower than the
outboard side [37], which is again consistent with ballooning-like turbulence.
1.2
1.2.1
Impurities
The effect of impurities on the plasma
Impurities are defined as any element other than the deuterium/tritium fuel
that composes the main chamber plasma, this includes the helium ash that
is the result of the D-T fusion reaction. The main effect of these impurities is
to cool the plasma via radiation, which directly affects plasma performance.
The radiation from any given element is highly dependent on the charge
on that element and the plasma temperature. Generally, higher Z impurities
radiate more than lower Z impurities and so are undesirable in a fusion device.
For fully ionised impurities radiation is caused by Bremsstrahlung losses due
to collisions with electrons and ions and is approximately given by [38]
Wb = 0.5 × 10−24 ne ni Z 2 T 1/2 W/m3
(1.9)
The Z 2 dependence immediately shows the problem of high Z impurities.
To add to this, high Z impurities are more likely to retain some of their inner
electrons, even at the high energies found in tokamak plasmas (≈ 10keV ).
This allows radiation due to excitation of electrons and provides a much
higher radiative efficiency.
As well as cooling by radiation the impurity ions can cause an effect
known as fuel dilution. The plasma β, the total plasma pressure over the
magnetic pressure B 2 /2µ0 cannot exceed the Troyon β-limit[6]
10
1.2 Impurities
βmax [%] =
2.8Ip
aB
(1.10)
As all electrons and ions contribute to the plasma pressure and therefore
β the increased number of electrons from high Z impurities can quickly cause
the plasma to approach this limit, even for low impurity fractions.
Low-Z impurities can also cause current profile contraction due to radiation near the plasma edge, where the temperatures are relatively low and
some electrons can remain bound to the impurity ion. This potentially strong
radiation can reduce the plasma conductivity to a point where the current
profile contracts causing high current gradients inside the q=2 surface[6]
which can then lead to plasma instabilities.
As well as these negative effects impurities can also be beneficial, notably
by radiative cooling of the SOL, reducing the heat load on the divertor targets. Radiative cooling of the H-mode pedestal via impurities has also been
used to control the heat load on the targets due to Edge Localised Modes
(ELMs) [39].
1.2.2
Impurity generation
Impurities in tokamaks are primarily generated by either chemical or physical sputtering. Physical sputtering is the principle mechanism in impurity
generation and occurs when an energetic particle striking a solid surface
transfers enough momentum to eject an atom from the solid lattice. This
process occurs on all plasma wetted areas but can also occur on surfaces a
large distance away from the main plasma due to the escape of energetic
charge-exchange neutrals. Lower energy particles can cause chemical sputtering when impacting on a carbon surface, the chemical potential energy of
hydrogenic or oxygen atoms or ions can break carbon bonds and allow the
11
1.2 Impurities
creation of C − D or other reactive compounds. This can easily result in the
emission of volatiles such as CH4 . In cool dense divertor plasmas chemical
sputtering can in fact dominate over physical sputtering[40]. Once an impurity has entered the main plasma it is likely at some point to return to the
wall, potentially resulting in self-sputtering and increasing the impurity content of the plasma. Gaseous impurities can also add to the impurity source
through recycling at the targets.
As well as impurities entering the plasma from vessel structures there
exists a completely unavoidable source of impurities in any burning plasma.
Helium produced by the D-T reaction is an unwanted impurity in the bulk
plasma and as a gas is also recycled at the targets. This is a serious problem
for future burning plasma devices due to the conflicting requirements to
reduce the impurity source to the main plasma while attempting to remove
helium ash.
1.2.3
Impurity transport
Stangeby[5] provides a useful analysis of the primary forces acting on impurities parallel to the magnetic field. A basic treatment leads to five force terms
acting on the plasma, the electrostatic force, the pressure gradient force, a
friction force and forces due to ion and electron gradients.
FZ = ZeE −
1 dpZ
(vi − vZ )
d(kTe )
d(kTi )
+ mZ
+ αe
+ βi
+ ...
nZ ds
τs
ds
ds
(1.11)
where Z is the impurity species atomic number, nZ is the impurity species
density in particles/m3 , pZ the impurity pressure in P a, vi and vZ are the
hydrogenic ion and impurity ion velocities respectively, τs is the impurity
stopping time, Te and Ti are the electron and ion temperatures, s is the
12
1.2 Impurities
parallel distance along the field line and αe and βi are coefficients that depend
primarily on Z.
The electrostatic force ZeE is simply the force exerted on the charged
impurity ions by the parallel electric field present in the SOL. The pressure
gradient force − n1Z dpdsZ acts in the direction opposite to ∇PZ due to the
imbalance of pressure on each side of a given volume. The friction force
Z)
is due to the background flow of the hydrogenic plasma and acts
mZ (vi −v
τs
in the same direction as the flow, generally towards the targets.
The final two terms are slightly less intuitive and are due to the collision
cross-section and hence collision frequency between impurities and either
electrons or hydrogenic ions having an inverse dependence on temperature.
Ions or electrons colliding with the impurity ions will have travelled on average λii or λee since their last collision with another similar species, meaning
that the average temperature and therefore collision frequency for ions or
electrons impacting the impurity ions from the cooler side will be higher and
more momentum will be transferred than for ions or electrons impacting from
the hotter side. This drives impurity ions up the temperature gradient, in
general away from the targets, see figure 1.1
A more rigorous treatment of these forces is presented by Spitzer [41], in
which collisions between particles are dealt with from first principles. However the Spitzer treatment assumes a constant temperature plasma and so
does not include the ion and electron temperature gradient terms. A more
detailed treatment including temperature gradients has been carried out by
Reiser[42] that includes these terms.
13
1.3 Plasma boundary diagnostics and experimental techniques
Figure 1.1: The temperature gradient force drives impurities up the temperature gradient. Ions and electrons impacting the impurity ion Z from the
lower temperature side will have lower average temperatures and collision
frequency than ions and electrons from the hotter side. They will therefore
transfer less momentum to the impurity ion resulting in a net force F in the
direction of increasing temperature.
1.3
Plasma boundary diagnostics and experimental techniques
1.3.1
Principle plasma boundary diagnostics
A variety of diagnostics are used in the edge plasma, the three most common
techniques, Langmuir probes, spectroscopic imaging and Thomson scattering
are described below.
Langmuir probes
A sufficiently negatively biased surface in contact with the plasma will repel
i
all electrons, positive ions will flow to the surface causing a current jsat
that
14
1.3 Plasma boundary diagnostics and experimental techniques
is independent of the applied voltage. Assuming Ti = Te this saturation
current is given by
i
= ene cs
jsat
(1.12)
As the bias is increased electrons begin to reach the surface and the
net current decreases until it reaches zero at the floating potential Vf when
ji = je . The measured current is given by
I = (ji + je )A = ji (1 − exp(e(V − Vf )/Te ))A
(1.13)
where A is the projected area of the probe, V is the bias voltage relative
to the plasma and ji , je are the current densities due to electrons and ions.
As the voltage is further increased ions are prevented from reaching the
surface and an electron saturation current is reached. By sweeping the bias
voltage one can determine the electron temperature and density. This is the
single electrode Langmuir probe, double and triple probe configurations are
also possible where probes are biased to different levels with respect to each
other.
Langmuir probes are cheap and robust and provide one of the most important tokamak diagnostics. Several hundred may be found located in the
typical tokamak divertor and they provide valuable information for experiment and modelling. Reciprocating probes also allow the use of Langmuir
probes inside the SOL, however the probe itself will perturb the plasma and
can only be in contact with the plasma for short periods of time.
A pair of Langmuir probes aligned with B and with the collection faces
pointing outwards along the field allow one to make an estimate of parallel
flow in the SOL. This technique relies on the premise that the ion current
will be greater for the probe facing into the plasma flow. The ratio of the
15
1.3 Plasma boundary diagnostics and experimental techniques
upstream to downstream current being a function of the ratio of the flow
velocity to the ion sound speed. Langmuir probes in this configuration are
known as Mach probes. Mach probe measurements are however subject to
significant errors and care must be taken in their interpretation[43].
Thomson scattering
Several non-invasive methods exist for probing the SOL. One of the most
common of these is Thomson scattering, powerful infra-red or visible lasers
are fired into the plasma and the light scattered from electrons is detected by
spectroscopically filtered cameras. The total intensity of the scattered light is
proportional to the plasma density and the electron temperature is calculated
from the observed Doppler broadening of the scattered light due to the electron thermal motion. Thomson scattering systems exist on many tokamaks
and typically provide electron temperature and density profile measurements
at resolutions better than 1cm [44, 45].
Spectroscopic imaging
At the relatively cool temperatures in the SOL plasma emission is predominantly in the visible spectrum. This makes spectroscopic investigation of
the SOL particularly useful. First the deuterium confinement time can be
obtained by measuring the Dα line intensity and assuming that the rate of
recombination is much less than the ionisation rate in the SOL. The effective plasma atomic number Zef f can also be determined by measuring the
background Bremsstrahlung radiation, which is a function of electron temperature, density and Zef f . Aside from these two techniques edge line emission
provides valuable information. Charge exchange between plasma ions, impurities or heating or diagnostic beams provides a measurement of Ti . Doppler
16
1.3 Plasma boundary diagnostics and experimental techniques
broadening and shifting of emission lines provides information on Ti , plasma
rotation and SOL flow. Emission from impurities allows spatially resolved
measurements of both impurity temperature and density as well as providing
information on impurity transport and plasma flow. Helium and lithium are
typically used in diagnostic beams while carbon has several strong visible
lines, particularly CII at 514nm and CIII at 465nm. The presence of carbon
in standard plasmas and the existence of these lines makes carbon a particularly useful tool in studying plasma flow. Modern fast cameras are able to
image the emission on microsecond timescales and several experiments have
been carried out using impurity injection to probe plasma flow, see section
1.3.2.
Other edge diagnostics
Aside from the diagnostics mentioned above a whole range of options exist
for diagnosing the edge plasma. These include bolometer arrays for the measurement of radiated power, charge exchange recombination spectroscopy for
density and temperature profiles of low Z impurities, reflectometry for edge
density profiles and turbulence measurements, interferometry for integrated
electron density measurements and divertor pressure gauges. Spectroscopic
imaging of Lithium and Helium beams also provide measurements of temperature and density
Coherence imaging spectroscopy
Accurate measurements of plasma flow are particularly hard to achieve, Mach
probes, already described here in 1.3.1 perturb the plasma and have a large
measurement error. A method for passive measurements of plasma flow has
been developed on the DIII-D tokamak using coherence imaging [46–48]. This
17
1.3 Plasma boundary diagnostics and experimental techniques
technique uses an imaging 2 beam interferometer; a fixed delay is introduced
between the two beams at all positions on a 2D image of the plasma. An
additional delay is then added which varies along one image direction and
results in a set of parallel fringes superimposed on the image. Any phase
change due to Doppler shifts arising from plasma flow cause a distortion in
these fringes and comparison with an un-distorted calibration pattern using
FFT techniques yields flow information. It should be noted that the spatial
resolution differs between the horizontal and vertical directions, assuming
the variable delay is introduced horizontally the vertical resolution is defined
by the scale of the fringes which can be many pixels.
1.3.2
Impurity injection experiments
Stangeby [5] categorises impurity injection experiments into those using recycling and non-recycling elements. Experiments using recycling gases such
as helium and argon are usually concerned with gaining an understanding
of impurity retention and pumping. Obtaining information about local conditions is more difficult due to the competition between the injected source
and any recycling that occurs after this, although valuable information can
still be gained [49]. Experiments using non-recycling impurities can provide measurements of the parallel and poloidal drift velocities [50–52] and
directly show the level of impurity screening and whether impurities can become trapped in the SOL [53, 54]. The primary method used for these types
of studies is 2 dimensional spectroscopic imaging of the lower charge states
of the impurity used. Carbon has been the most commonly used impurity
due to its prevalence in many tokamaks, the ease with which it forms gaseous
compounds with hydrogenic elements, the existence of strong visible emission
lines and the availability of the carbon-13 isotope which allows postmortem
18
1.3 Plasma boundary diagnostics and experimental techniques
examination of carbon deposition from injected carbon.
Edge impurity injection experiments have been carried out on a range
of tokamaks including DITE[54], TEXT[55], Alcator C-Mod[51], DIII-D[56],
ASDEX Upgrade[57, 58], JET[59] and TEXTOR[60]. Various techniques are
used and a selection of these are briefly discussed below.
Gas injection
Gas injection systems designed to inject trace quantities of gas into the SOL
have been installed on several tokamaks. Recent experiments have been
carried out on both Alcator C-Mod and DII-D using impurity injection for
the study of local impurity transport and SOL flows. On Alcator C-Mod
Gangadhara et al.[51] used a reciprocating fast scanning probe[61] to inject
deuterated ethylene (C2 D4 ) into the SOL at various depths. The gas injection had a typical duration of 10ms and injected approximately ≈ 5 × 1016
molecules, resulting in ≈ 1017 carbon atoms. The carbon II and III lines
where then imaged using gated CCD cameras. The aim of this study was
to compare data obtained from the plume imaging with data previously obtained from fast scanning Langmuir/Mach probes, specifically to improve
the understanding of parallel and E × B flows that affect the transport of
impurities into the bulk plasma. The results clearly showed that the surface
of the probe had a significant effect on the plume structure, causing jetting
parallel to the local magnetic field. Transport modelling that includes this
effect suggests that values for Er obtained using probes are in error and that
probes over-estimate the parallel flow to the divertor in the far SOL, suggesting that main chamber recycling and not target recycling is the dominant
process in the Alcator C-Mod SOL.
A different approach has been taken at DIII-D where a Porous Plug Injec-
19
1.3 Plasma boundary diagnostics and experimental techniques
tor (PPI)[56, 62] has been developed that mimics the carbon impurity source
due to chemical sputtering. This is achieved by siting a gas injector behind
a porous graphite cap of diameter 4.2cm that has a regular square lattice
of 1004 0.25mm holes drilled into its surface. This injector is mounted on
the divertor materials evaluation system (DiMES) near the outer strike point
in the DIII-D divertor. This allows a diffuse cloud of methane molecules to
be injected into the divertor at an energy of approximately 0.05eV, similar
to that expected from chemically sputtered hydrocarbons. The injection is
distributed over an area that is large relative to the mean free path of the
plasma-molecular processes being studied, allowing detailed studies of the
photon emission of CH4 molecules injected at known flow rates. This experiment has confirmed that the intrinsic chemical erosion yield is close to that
measured in the laboratory.
Several experiments using gas injection have been carried out on ASDEX
Upgrade [52, 58, 63] using
13
CH4 . In these experiments gas is injected into
the lower divertor at the end of a campaign, a selection of tiles close to the
injection location is then removed and the deposition of carbon-13 studied.
Differences in deposition are highlighted for forward and reversed fields [52],
between H-mode and L-mode discharges[58] and for graphite and tungsten
tiles[63]. These differences can be attributed to the effect of the E × B and
B × ∇B forces and to the effect of surface roughness in the case of the
different tile types. For certain L-mode shots significant upstream transport
is observed which is not observed in either H-mode shots or when using lower
puffing rates[58]. Carbon-12 has also been used on several machines [64–66]
to study hydrocarbon fluxes and erosion yields by spectroscopic imaging of
injected carbon.
Impurity injection experiments aiming to understand the levels of impu-
20
1.3 Plasma boundary diagnostics and experimental techniques
rities reaching the core due to chemical sputtering have also been carried
out, an example of this being the studies on JET[59, 67]. The more recent of
these[59] used methane injected from several ports in the JET divertor and
midplane and at the top of the vessel. The core carbon content was then
measured using charge exchange recombination spectroscopy and Zef f measurements from visible Bremsstrahlung. The experiment was performed in
a range of L-mode and H-mode plasma conditions and the carbon injection
and transport to the core was modelled using the DIVIMP and EDGE2D
codes (see section 1.4. Various observations were then made including increased penetration to the core from the private flux region compared to the
rest of the SOL and increased penetration for limiter plasmas. It was also
noted that close to the separatrix carbon transport is dominated by diffusion while further out it is dominated by parallel flow. It should be noted
that this approach is fundamentally different to the other two methods mentioned previously as it does not use data on local SOL transport and relies
completely on modelling to infer transport properties. Similar experiments
designed to study the bulk penetration of gases such as neon and argon into
the core have also been performed on JET[68]. These elements are likely
to be used on future machines to reduce the power loading to the divertor
through impurity seeding [39].
A supersonic gas injector[69] was developed for use on the NSTX[70]
spherical tokamak. This injector was intended for both fuelling and diagnostic applications and is capable of injecting up to 1022 particles per second at
velocities up to Mach 4 into the edge plasma.
21
1.3 Plasma boundary diagnostics and experimental techniques
Laser ablation and sublimation
Gas injection systems are intrinsically limited in the impurities that they can
inject. They are also unable to inject impurities on very short timescales.
Laser ablation systems are able to inject a variety of solid materials by focusing a high power laser beam onto a target inside the tokamak over very
short timescales.
The laser ablation system on JET has been used to inject Tungsten,
Hafnium and Nickel[71–73]. The system uses a ruby laser to fire pulses of
up to 10J at a target positioned on the vessel wall, typically 1018 particles
are ablated into the chamber, with around 5% of the particles reaching the
plasma core. This system provides important information on core impurity
transport and penetration, however the influx of high Z particles is highly
perturbing and provides limited information on local edge transport. Experiments using laser ablation have also been carried out on several other
machines including ASDEX Upgrade[74], TCV[75] and TEXT[55]. Experiments using laser ablation tend to rely heavily on spectroscopic imaging of
the impurity emission, for heavy elements this emission is generally in the
UV and X-ray, this and the complexity of the spectra make this area of work
extremely challenging.
Silicon has been injected into ASDEX Upgrade using the Laser-blowoff technique in order to study core transport[74]. A significant increase in
core transport is observed in plasmas with central electron-cyclotron heating,
which is promising as a method for helium ash extraction in a burning reactor. A novel method for the injection of small quantities of high Z material
has also been developed on ASDEX Upgrade[76]. A small heated chamber
mounted on a probe head allows small quantities of suitable materials to be
sublimated and then injected into the plasma. This allows high Z materi-
22
1.4 Modelling Impurities in the Scrape-Off Layer
als to be injected in controllable quantities, although still over a relatively
long timescale. Tungsten carbonyl [W (CO)6 ] was used in experiment, this
allows the tungsten particle flux to be accurately estimated by observing the
emission from the carbon and oxygen ions.
1.4
Modelling Impurities in the Scrape-Off
Layer
1.4.1
Approaches to Impurity Modelling
Two basic approaches are generally employed when modelling impurities in
the edge plasma. The first of these is to use a multi-fluid approach and
treat both the hydrogenic background plasma and the impurity particles as
fluids. This approach has the disadvantage that impurities in lower charge
states tend to exist only for a very short time and so are not in thermal
equilibrium with the background plasma[42], these approaches can also be
computationally very expensive[77]. However they do include the effect of the
impurities themselves on the edge plasma and are therefore valuable tools.
The other approach is to model the background plasma as a fluid, with or
without the effect of neutrals and impurities, and then adopt a fully kinetic
treatment for the impurity particles to be studied[78].
1.4.2
The Two-Point Model
The simplest approach to modelling the SOL while neglecting impurities uses
two reference points, one at the target t and the other upstream at or close
to the LCFS (u). This is known as the Two-Point model[12, 79] and despite
its simplicity is able to replicate many observed plasma conditions[80]. The
23
1.4 Modelling Impurities in the Scrape-Off Layer
upstream location can be taken as half way between the targets (assuming a
single null divertor plasma) or at the midplane, the choice of location does
not have a significant effect on the results.
Three basic assumptions are used in the two point model[5]:
1. Recycling neutrals are re-ionised in a thin layer close to the targets on
the same field line as followed by the original ion that impacted the
target. There is also no parallel flow along most of the SOL and no
cross-field flow.
2. There is no friction between the plasma and the targets and no viscous
effects so that the total pressure is constant along the flux tube.
3. The parallel power flux density is carried solely by conduction.
Following Stangeby these assumptions lead to a set of three equations
containing three unknowns nt , Tt , Tu ,
2nt Tt = nu Tu
7/2
Tu7/2 = Tt
+
7 qk L
2 κ0e
qk = γnt kTt cst
(1.14)
(1.15)
(1.16)
with the specified constants L being the distance between the two points
along the magnetic field, κ0e the electron parallel conductivity coefficient and
γ the sheath heat transmission coefficient. cst is the sound speed at the target
and the control parameters nu and qk are the upstream density and parallel
power flux density.
24
1.4 Modelling Impurities in the Scrape-Off Layer
It is possible to extend this basic model to include radiative and charge
exchange power loss, momentum loss due to friction and viscous forces, nonzero parallel heat convection and energy lost by electrons re-ionising recycled
neutrals, these extensions are described by Stangeby.
1.4.3
1D fluid modelling along B
The complexity of modelling the SOL essentially increases with the number
of dimensions that one chooses to model. The two point model described
above is a zero dimensional model, no attempt is made to model the relevant
parameters as a function of parallel distance sk along the SOL. In order to
model these parameters one starts with the one dimensional velocity distribution given by the Fokker-Planck kinetic vector equation [5, 81]
vx
∂f
eE ∂f
∂f +
=
+ S(x, v)
∂x
m ∂vx
∂t coll
(1.17)
where ∂f /∂t|coll is the change due to collisions other than events where
particles are created or destroyed and S is the difference between particle creation and destruction rates. Taking moments of this equation by multiplying
by dv, mvx dv, 21 mvx2 dv, etc. and integrating results in a set of fluid equations
that describe the plasma in 1-dimension. A brief derivation of these can be
found in Stangeby but they can be summarised by a set of three conservation
equations in three unknowns n, v, T by assuming Te = Ti and p = pe + pi and
ignoring viscous stress,
Particle conservation
d
[nv] = Sp
dx
(1.18)
d
[(mi v 2 + 2kT )n] = −mi vσ̄v̄in nnn
dx
(1.19)
Momentum conservation
25
1.4 Modelling Impurities in the Scrape-Off Layer
Energy conservation
d 1
2
5/2 dTe
(mi v + 5kT )nv − κ0e Te
= QR + QE
dx 2
dx
(1.20)
where Sp is the net particle source, QR is the heating source due to net particle drift and QE is the power source due to hydrogenic recycling. These fluid
equations require significantly less computational time to perform, however
further approximations are required in order to close the equations. Ignoring
heat conduction qk allows one to do this. When self-collisionality is high
the particle distribution tends to Maxwellian and qk → 0, the equations then
close with only convection appearing in the energy equation. When collisionality is lower an approximation can be made of qkcond = −κ0 T 5/2 dT /dx this
works for moderate collisionality but fails as collisionality becomes small.
For a rigorous treatment in this regime it is necessary to calculate higher
moments of the kinetic equation that may then be approximated in order to
close the system.
When using these equations for modelling in one dimension it is common
to view the SOL as being in one of two regimes, either sheath limited or
conduction limited. The defining property of these regimes is the existence
or lack of a significant parallel temperature gradient in the SOL.
The Sheath Limited Regime
The sheath limited regime is characterised by the absence of parallel temperature gradients in the SOL and low collisionality. For a given particle
and power source from the bulk plasma the sheath at the targets defines the
conditions in the SOL. This situation can occur without the need for parallel
flow, high parallel conductivity and small temperature gradients can transmit all the power from the bulk plasma to the targets. For the case of low
26
1.4 Modelling Impurities in the Scrape-Off Layer
heat conductivity it is parallel flow that must carry this power. It should be
noted that Ti need not be constant, assuming that the assumption of Ti = Te
is dropped.
The Conduction Limited Regime
In the absence of strong convective flows parallel conduction can become
the limiting factor for the SOL properties although the sheath still plays an
important role. Due to the lack of significant flow, recycling ionisation is
assumed to occur very close to the targets so any flows that are present are
confined to a thin region close to the targets. Large temperature gradients
characterise this regime.
When modelling the sheath limited regime the obvious assumption to
make is to treat Te and Ti as constant parameters that can be obtained by
some other means than the fluid equations. The energy conservation equation is not then required and ignoring collisions the particle and momentum
conservation equations become
d
(nv) = Sp
dx
(1.21)
d
(mi nv 2 + nkTi + nkTe ) = 0
dx
(1.22)
Plasma parameters calculated from these simplified equations agree surprisingly well with full kinetic treatments[5, 82], particularly considering that
this system is completely collisionless.
In the conduction limited regime the isothermal assumption is invalid and
parallel heat conduction is dominant. The choice of boundary conditions then
becomes critical in this regime. It is possible to specify these boundary conditions entirely at the target and Langmuir probes(1.3.1) incorporated into
27
1.4 Modelling Impurities in the Scrape-Off Layer
the target provide both density and temperature information. Other diagnostics such as Thomson scattering can then be used to further constrain the
solution at other points along the SOL. The question of particle, momentum
and energy sources also becomes more complicated in the conduction limited regime and it is usually necessary to employ a Monte-Carlo neutral code
such as EIRENE[83] to calculate these sources. The effect of impurities, in
particular radiation, can be dealt with in a similar way using a dedicated
impurity code such as DIVIMP[84].
1.4.4
Modelling the SOL in 2 dimensions
Modelling of the SOL in 1 dimension naturally neglects any cross-field processes that occur. Several codes exist that use a multi-fluid approach to
model the SOL in 2 dimensions and include the cross-field drift and diffusion
terms that the 1 dimensional approach does not, notable examples being
SOLPS[77, 85], EDGE2D[86, 87] and UEDGE[88, 89]. For all of these codes
toroidal symmetry is assumed and the remaining 2 dimensions are radial
and either along B or the projection of the parallel direction in the poloidal
plane. The necessary boundary conditions for these codes are complex and
great care must be taken at the four boundaries, the two targets, the LCFS
and the outer SOL or first wall. It is also necessary to specify values for the
anomalous cross field transport coefficients.
The SOLPS package primarily consists of the B2 multi-fluid code[77] and
the EIRENE neutral particle Monte-Carlo code[90]. It has been used extensively on many tokamaks[91–94] and is one of the principle tools for SOL
modelling. Stangeby [95] has used SOLPS to form a simple relationship
between upstream electron density and temperature decay widths and the
power width in the divertor, a vital parameter in the operation of ITER.
28
1.4 Modelling Impurities in the Scrape-Off Layer
Studies carried out on ASDEX Upgrade[96] have also used SOLPS to understand the effect of cross-field drifts on plasma flow and target conditions
in the SOL, showing good agreement between simulation and experiment in
the low-recycling regime. SOLPS has also been used to study divertor detachment on ASDEX Upgrade and DIII-D[97], concluding that our current
understanding does not allow effective simulations of detached conditions.
EDGE2D also comprises a multi-fluid plasma solver coupled to a MonteCarlo neutral code, although there exists the choice of either EIRENE or
an alternative neutral code NIMBUS[87]. This code has been primarily
used on the JET tokamak although it has also been applied to ASDEX
Upgrade[98] and used as a predictive tool for future devices [99, 100]. Its
use on JET however has been extensive, studying the edge temperature and
density profiles[101], SOL flows [43], migration of carbon-13[102], the effect
of atomic processes on detachment [103] and in-out asymmetry[104]. Results
from the code are also used in cross-code comparisons[105] that help improve
the reliability of simulation results.
The majority of work using the UEDGE code has used data from the
DIII-D tokamak. This has included scenario development[106], studies on
visible carbon emission[107], the dependency of the behaviour of injected
argon on the up-down magnetic balance in double null plasmas[108], studies
of plasma wall interaction in the presence of ELMs[109], the effect of E × B
drifts on the transport of intrinsic impurities[110] and the importance of edge
transport on core carbon concentrations[111].
UEDGE has also been used in multi-machine studies, such as Groth[112]
who showed the necessity of the inclusion of cross-field drifts to model divertor particle and heat loads on DIII-D ASDEX Upgrade and JET. In this
work enhanced chemical sputtering yields were also required to closely repli-
29
1.4 Modelling Impurities in the Scrape-Off Layer
cate observed conditions although these enhanced factors may conceal the
fact that some other mechanism is inadequately modelled. The simulated
flow was also shown to be incorrect on the machines studied, although this
issue is also frequently the case for other edge codes. Detachment in the
snowflake divertor on the spherical tokamak NSTX has also been studied using UEDGE[113] where a gas power loss mechanism was identified that may
contribute to the high recycling seen in the snow-flake divertor simulation.
This work also highlighted the need to improve the DEGAS neutral model
used in the code. ITER simulations to study the effect of a 2nd X-point have
also been carried out[114].
1.4.5
The Onion Skin Method
Sitting between the 1 and 2 dimensional approaches described above is a
modelling technique known as the the Onion-Skin Method, which relies on
the assumption that the 1 dimensional conservation equations are valid over
a finite radial extent. This method treats the boundary plasma as a sequence
of nested flux tubes (fig. 1.2) and applies a suitable SOL model along B for
each tube. This model can be anything from a simple two-point model to
a comprehensive 1D model that solves the 1D conservation equations along
B and includes volumetric sources and sinks for particle momentum and energy. Boundary conditions are set for each tube, usually at the targets from
Langmuir probe data although upstream measurements from other diagnostics can also be used. This essentially results in a 2D solution derived from
the 1D solutions for each flux tube.
Each flux tube is considered independently with no perpendicular transport between the tubes, this is a marked difference with a full 2-D code. In
the 2-D approach the cross-field diffusivity must be set as an input param-
30
1.4 Modelling Impurities in the Scrape-Off Layer
Figure 1.2: A typical onion skin geometry in the poloidal plane from a MAST
plasma with the MAST first wall also plotted
eter, in OSM the cross-field fluxes can be extracted from the series of 1-D
solutions using the radial variations of density and temperature across the
target. An excess or deficit between the net particle source along a flux tube
and the particle outflow to the target is attributed to the cross field transport of particles, which is treated as sources and sinks along the length of
each tube[115]. The OSM 2-D plasma solution made up of the individual flux
tubes can be used as a background for neutral or impurity codes that provide
particle sources and sinks. The onion skin method can then be performed
iteratively with these codes to obtain the best plasma solution incorporating
31
1.4 Modelling Impurities in the Scrape-Off Layer
the effect of these sources and sinks. This approach provides a robust 2D
simulation of the plasma and compares favourably with full 2D models such
as EDGE2D[116].
A code based on the onion skin method and named OSM has been developed by Stangeby and Elder[84] and has been used on several machines. Neutral behaviour has been studied on Alcator C-Mod[117], cross field transport
in the SOL on JET[118], the effect of including SOL currents in the model
on MAST[119] and the midplane SOL conditions reconstructed on the EAST
tokamak. When compared to the more complex 2D codes the OSM approach
has the advantage of shorter run-times on the order of minutes compared to
hours, days or longer for the 2D approach, meaning it can potentially be used
for basic modelling during experiments. The extensive use of experimental
data in constraining the solution also simplifies the simulation process, so
that a reasonably reliable model of SOL conditions can be inferred quickly.
OSM does not currently include drift terms, casting some doubt on the validity of the solutions[120], particularly in spherical tokamaks where these
terms can be larger than in standard aspect ratio tokamaks.
1.4.6
Further SOL modelling
The development of ergodic divertors and a requirement for detailed modelling of plasma wall interactions for next generation devices such as ITER
has called for the use of 3D fluid codes such as EMC3[121, 122] and BOUT++[123].
Full kinetic treatments of the SOL remain prohibitive, however more recently
high performance computing environments have expanded the use of gyroaveraged kinetic treatments of the SOL plasma. Particle properties are averaged around a single gyro-orbit, removing the high frequency gyro-motion
that makes full kinetic treatments intractable. This guiding centre approach
32
1.4 Modelling Impurities in the Scrape-Off Layer
is used in massively parallel environments by several codes such as XGC[124],
TEMPEST[125], GENE[126], GS2[127], GEM[128] and COGENT[129]. The
coupling of these codes has also improved, with tools such as KEPLER[130]
being used to allow many dedicated codes to be coupled relatively easily.
1.4.7
Kinetic impurity models
The 2D and OSM methods both provide a plasma background which can
then be used as input to kinetic Monte-Carlo codes that follow impurity ions
such as ERO[131], IMPMC[132] and DIVIMP[84]. These codes all follow
impurity ions on the background plasma, including the transitions between
ionisation states. They are commonly used to simulate impurity injection as
the localised source means only a limited number of particles are required
to gather adequate statistics, reducing the computational requirements that
can become prohibitive when modelling a large domain in this manner.
ERO is often used with a background provided by SOLPS, and has been
used in a large number of studies on ASDEX Upgrade. Aho-Mantila[133]
showed that E × B drifts have a significant impact on the carbon migration
in the ASDEX Upgrade divertor. Carbon re-deposition was also studied
by Pugno[58] although these simulations did not include drift terms, which
appear necessary to account for the deposition patterns deviating from the
magnetic field direction. Makkonen[134] used ERO to study the flow of
carbon by injecting methane at the midplane and suspected temperature
gradient forces of driving flow towards the upper divertor in low density
cases.
ERO has also been used on other machines such as JT-60U[135], where it
was used to study asymmetry in divertor carbon deposition, TEXTOR[131],
where material erosion was studied, and JET[136] to study material migra-
33
1.4 Modelling Impurities in the Scrape-Off Layer
tion and erosion.
IMPMC is now included in the SONIC[137] package along with the twodimensional fluid code SOLDOR and neutral code NEUT2D[138]. These
codes have primarily been used on the JT-60U tokamak, Shimizu[139] and
Hoshino[140] have studied impurity transport in detached plasmas, and is
being used extensively in the design of the new JT-60SA tokamak[141–143]
The DIVIMP code has been used on a wide variety of machines with several plasma solvers being used to provide the background solution, although
it is commonly bundled with OSM in a package called OEDGE. Lisgo[117]
used this combination to study and improve the simulation of neutral behaviour in the C-mod divertor as well as studying detached plasmas in the
DIII-D divertor. McLean and Mu[144, 145] have also used OEDGE on DIII-D
to study CH4 injection experiments. Tungsten transport has been studied on
JET[146] using EDGE2D-EIRENE to provide the plasma solution, with this
work leading to the conclusion that extrinsic impurity seeding is required
to reduce the tungsten source and limit the core tungsten concentrations.
SOLPS has been used to provide background solutions in simulations of carbon injection into ASDEX Upgrade plasmas[134, 147]. These simulations
highlighted the importance of accurate modelling of the SOL flow, which is
believed to be a cause of discrepancies between the simulated and measured
carbon deposition. This combination has also been used to make predictions
for tungsten erosion and transport in ITER[148], showing that in divertor
plasma configurations running a tungsten divertor on ITER can maintain a
core tungsten concentration below that required for successful operation.
Drift terms are not included in DIVIMP, when run with OSM providing
the background plasma this means that significant physics is missing from
the model. The use of DIVIMP for ITER predictions further increases the
34
1.5 The MAST tokamak
importance of this omission. However the interpretive nature of OSM to
some extent mitigates the lack of these terms, especially in light of the poor
replication of plasma flow in current models.
1.5
The MAST tokamak
The Mega Amp Spherical Tokamak (MAST)[149] tokamak is a tight aspect
ratio spherical tokamak with typical major radius R = 0.85m and minor radius r = 0.5m. During normal operation the plasma has a maximum plasma
current Ip = 0.9M A and toroidal field BT = 0.52T measured at the magnetic axis. MAST typically operates in a double null divertor configuration.
The open nature of the spherical tokamak design allows excellent diagnostic
coverage of the plasma. As well as large arrays of divertor Langmuir probes
MAST has several viewing ports at different toroidal locations around the
machine, allowing comprehensive imaging of the plasma. A Thomson scattering system also provides measurements of both the core and edge plasma.
MAST pulses are often referred to as shots and are numbered using a sequential numbering system, at the time of writing the latest shot number is
30473. These numbers will be used to refer to a particular discharge.
The lower divertor includes a system named the Divertor Science Facility
(DSF)[150] for inserting samples and probes without any requirement to
vent the machine. This system permits electrical connections and allows
the installation of systems such as the impurity injector described here, a
Retarding Field Energy Analyser (RFEA)[151] and a sample holder for the
introduction of dust[150] in a single day during scheduled breaks in operation.
There are significant quantitative differences between spherical and the
more common large aspect ratio tokamaks, however there is no fundamental
35
1.5 The MAST tokamak
difference between the two designs. The achievable β (see section 1.2.1) is
significantly higher in spherical tokamaks due to a reduction in both ballooning and kink instabilities. The increased curvature also means that the radial
gradient of magnetic field is larger, resulting in stronger ∇B drifts which can
affect transport in the SOL. The plasma wetted area on the divertor surfaces is significantly smaller in a spherical tokamak due to the reduced major
radius. This means that the heat flux to the targets is higher for a given
total power, making the progression to reactor scale machines more difficult.
Results from experiments on spherical tokamaks are generally comparable to
those from large aspect ratio machines, and simulations can be carried out
on both using the same software[152].
36
CHAPTER
2
Carbon injector design and testing
2.1
Design motivation
Impurities have a significant effect on plasma performance and can also be
used to alleviate the problems of excessive heat loads on plasma facing components (see 1.2.1). An understanding of the transport of any impurities is
therefore of great importance in the design and operation of existing and
future tokamaks. The use of injected impurities in order to further this
understanding is discussed in section 1.3.2. The most common methods of
injection used in previous edge impurity transport experiments are laser ablation and the injection of impurity gases (section 1.3.2). For gas injection
the number of particles injected is often significant when compared to the
plasma density and the injected impurities significantly perturb the plasma.
The injection also occurs over a timescale that is greater than the typical SOL
37
2.2 The injector design
dwell time of the plasma so information on timescales shorter than this is
restricted. Laser ablation offers the option of very short plume duration and
accurate control of the number of ablated particles. However this method is
technically very difficult to achieve and expensive. Another method that has
been used previously on the START tokamak is that of ablation from arcs
occurring between electrodes composed of the impurity to be injected, this
work was unfortunately not published. Carbon is one of the more commonly
studied impurities due to its presence in the majority of tokamaks and strong
line emission and is also ideally suited for use as an electrode. Arcs can also
occur on very short timescales ≈ 1µs and the equipment required to produce
them is cheap and readily available. It was therefore decided that an injector
using a short duration arc would be designed to ablate carbon into the SOL
of the MAST tokamak. Data obtained from spectroscopic imaging and other
diagnostics would then be used to model the observed impurity transport.
2.2
2.2.1
The injector design
The spark head
The geometry of the electrodes has a significant effect on the nature and
result of an arc between them. The basic geometries one can envisage are
planar, cylindrical, concentric and spark plug type electrodes. These possibilities can be seen in figure 2.1. Concentric electrodes were chosen for the
prototype design as these have several advantages over the other geometries.
A schematic of this design can be seen in figure 2.2. Concentric electrodes
are simple to build and the inter-electrode gap remains stable under stress.
They also take advantage of the Marshall effect, described below.
38
2.3 Injector development
The Marshall Effect
A current discharge between concentric electrodes results in an axial force
on the ions and electrons making up the discharge. This effect was first
published by J Marshall in 1960 [153]. The magnetic field caused by the
current flowing along the central electrode causes a j × B force on the radial
discharge current in the same direction as the positive current, accelerating
the ions and electrons away from the electrode for both possible polarities.
A reasonable approximation for the impulse delivered to the plasma is given
by [153]
Z
Z
f dt = ln(r1 /r2 )
t
I 2 dt
(2.1)
t
where r1 and r2 are the outer radius of the inner electrode and inner
radius of the outer electrode respectively and I is the discharge current.
It should be noted that at the currents generated in the injector head the
typical magnetic field created is many times smaller than the typical field
of several Teslas found in tokamaks. Due to this the effect is expected to
be weak during operation within MAST but may be augmented at points
around the electrodes that are suitably aligned with the toroidal field.
2.3
2.3.1
Injector development
Test conditions
A dedicated vacuum chamber was built for the development and testing of
the injector. The chamber was largely constructed from components already
owned by the National Centre for Plasma Science and Technology. It uses a
TPH 240 ISO 100 Pfeiffer turbo pump and has a base pressure of 5×10−5 P a,
39
2.3 Injector development
significantly lower than the MAST divertor pressure (∼ 10−3 P a). Initial
testing was carried out using a capacitor bank of up to 20nF charged using an
Ultravolt 15A12P4-C power supply capable of delivering 15kV at 0.4mA. The
final design for use on MAST ran significantly lower voltages up to 2.5kV, this
limit was largely due to safety considerations imposed by the MAST team.
In order to accomplish breakdown at voltages below this limit a significantly
higher capacitance of 1.5µF was used in the final system. Triggering was
initially performed using a mechanical switch made in the laboratory, this
was later replaced with an Insulated Gate Bipolar Transistor(IGBT), see
section 2.4.2.
The outer electrode was made up of a carbon cylinder manufactured by
the MAST Special Techniques group. Cylinders of outer diameter 8mm and
inner diameter 3.1mm and 4.1mm allowed for testing of variable gaps between
the inner and outer electrode. The inner electrode consisted of carbon rods
that were available at DCU. For testing the concentric electrodes were fitted
into an SHV clamp connector, allowing easy interchange of the injector head,
see figure 2.3. An aluminium oxide sleeve was used as the insulator between
the two electrodes. This sleeve allowed the end of the electrodes to protrude
by 1-5mm, providing the spark gap itself.
2.3.2
Observed pressure increase
Large pressure increases in the vacuum chamber were observed after the test
discharges, figure 2.4. Although variable, this pressure increase was dependent on the chamber pressure and both the capacitance and voltage used.
The increase was measured using a Tektronix TD3000 oscilloscope connected
to a Pfeiffer ion-combi gauge. The initial rise occurred over a timescale of
100ms immediately after each discharge, this leads to the conclusion that
40
2.3 Injector development
Figure 2.1: Possible electrode geometries
Figure 2.3: The carbon electrodes of
Figure 2.2: Conceptual design for the the injector head fitted to an SHV
carbon injector
clamp connector
41
2.3 Injector development
the increase was due to material ablated from the injector. However, ablated
carbon is likely to stick to any surface it encounters so is unlikely to have
diffused to the pressure gauge mounted at the end of a short KF25 elbow
tube mounted above the chamber. The pressure increase was then suspected
to be due to hydrogen and oxygen from the dissociation of water present
on the injector head. This was then confirmed by using a mass spectrometer attached to the vacuum vessel, a significant increase in both hydrogen
and oxygen was observed after each discharge, although a small increase in
the carbon content was also observed. This is also consistent with the dependence on voltage and capacitance, the higher the energy released during
discharge the more water is dissociated.
~100ms
-6
~5x10 mbar
Figure 2.4: Pressure increase observed after a 10kV 20nF discharge
This presented a significant issue regarding the sparker operation on
MAST where there is essentially zero water content. If it is the water initiating the breakdown then the system would not work on MAST or any other
tokamak. In order to test this efforts were made to reduce the water content
in the chamber, which was measured using a Pfeiffer QMS200 mass spectrometer. While at atmosphere the vessel was baked to remove water from
the walls, the vessel was purged with a flow of nitrogen and then pumped
down, finally the vessel was cooled to cause the water vapour to condense
42
2.3 Injector development
on the chamber walls. This only partially succeeded in reducing the water
content although the chamber pressure was reduced to 3 × 10−5 P a. At this
pressure the mono layer formation time is approximately 4s, using the relation τmlf ≈ 4/P [154], this allows the possibility of testing the discharge in
the absence of water by repeatedly firing the injector at a frequency greater
than 1Hz, effectively cleaning the injector head and not allowing for the
formation of a water layer before each discharge. The injector continued to
break down in these conditions verifying that breakdown was possible in the
absence of a water layer. The associated pressure increase also decreased
after the initial discharges, showing that water dissociation associated with
the discharge was significantly decreased and attributable to water existing
as vapour close to the injector head.
2.3.3
Ablated mass measurements
The most important parameter of most injection systems is the quantity
of material injected. This can be measured using quartz crystal monitors
placed in front of the injector (figure 2.5, carbon ablated from the injector
then adheres to the face of the quartz crystal, changing its resonant frequency.
The frequency shift for a rigid mass evenly deposited onto the crystal is given
by the Sauerbrey equation[155]
∆f ≈
−2∆mf0
√
A ρq µq
(2.2)
for ∆f /f0 < 2%. Where f0 is the resonant frequency, ∆f is the change in
frequency, ∆m is the change in mass, A is the piezo-electric active area, ρq is
the density of quartz (2.648 × 103 kgm−3 ) and µq is the shear modulus of the
crystal (2.947 × 1010 kgm−1 s−2 ). The crystals were mounted in a specially
made probe that can be seen in figure 2.5.
43
2.3 Injector development
An intellimetrics IL150 Quartz Crystal Growth Rate Monitor was used
to drive the crystal and the thickness measurements were then converted
into masses. There are large uncertainties in the plume size and quantity of
carbon sticking to the crystal surface, however a lower limit can be placed on
the mass of carbon ablated by each discharge. The dependency of ablated
mass on the discharge voltage and stored charge can also be investigated.
The IL150 provides a measure of deposited thickness in nanometres, in
order to translate this measure into a mass it was assumed that the ablated
carbon formed a uniform coating on the monitor. Although this is clearly
not the case the uncertainties already present in the measurement make this
a reasonable assumption. The portion of the crystal exposed to the plume is
circular with diameter 8mm, making a total area of approximately 50mm2 .
The IL150 takes as input the density of the deposited material and this was
set at the density of amorphous carbon 2g.cm−3 in the units used by the
IL150. This gives an ablated mass of ≈ 10−7 g/nm, equivalent to 6 × 1015
atoms/nm.
Using the lossy mechanical switch deposition experiments were carried
out using 3-5kV and a capacitance of 200nF, equating to a stored energy
of up to 2.5J. No magnetic fields were applied to the plasma. Due to the
low sensitivity of the monitor crystal 5 shots were performed before each
measurement. A series of shots were also performed immediately before the
measurements in order to remove any water layer that may have formed on
the injector head. At 3kV no breakdown occurred however breakdown did
occur at 3.5kV. At 4kV the average deposition for each pulse was 0.04nm
while at 5kV the average deposition was 0.06nm. This equates to 2.4 × 1014
particles at 4kV and 3.6 × 1024 particles at 5kV.
44
2.3 Injector development
2.3.4
Imaging
High speed imaging of the plume was also carried out in order to confirm
the plume duration and extent. An Andor DH5H7 18F 03 single shot visible
camera was used to image the plume at different times during the discharge.
The camera was triggered using a Stanford DG535 pulse delay generator
connected to a C-T current monitor located between the capacitor bank and
the spark head. The delay was varied from 0ns to 3000ns and the integration
time from 5ns to 60ns. A capacitor bank of 20nF was used at a voltage of 8kV
giving a stored energy of 0.64J. The extent of the plume is very limited, up to
5mm, however it is expected that the extent will increase as the capacitance
used is increased towards 1µF . Looking at figure 2.6, the duration of the
plume can be seen to be less than 3ms, figure 2.6 shows the last remnants of
the plume. This duration matches the duration of the current pulse measured
using a Bergoz C-T current monitor, see figure 2.7.
Scanning electron microscopy and energy dispersive X-ray spectroscopy
A significant concern raised by the MAST team was that of contamination
of the vessel by the injector. In order to verify the purity of the ablated
material the crystal used for ablated mass measurements was subjected to
Energy Dispersive X-Ray spectroscopy (EDX) once a significant carbon layer
had been built up. Spectrograms taken with beam energies of 10 and 20kV
can be seen in figure 2.8. The depth of penetration of the beam is dependant
on the energy of the beam, the gold line seen in figure 2.8 b is due to the
beam penetrating through the thin layer of deposited carbon and interacting
with the gold substrate of the crystal. The 10kV spectrogram can therefore
be taken to be that of the carbon layer on the crystal. The only significant
45
2.3 Injector development
(a)
(b)
Figure 2.5: a) Probe containing a quartz crystal, the discolouring evident
on the crystal surface is due to ablated carbon. b) Side on schematic of the
quartz crystal placed in front of the injector head for ablation measurements.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 2.6: Visible images at 0, 50, 500, 1000, 2000 and 3000 nanoseconds
after the beginning of the discharge. Figures a to d were taken with a 40ns
integration time and figures e and f with a 20ns integration time. Each image
is 10mm by 10mm in the plane of the injector head which is on the right hand
side of each image.
46
2.4 Final design
non-carbon element detected is fluorine and this is likely to be due to contamination from the atmosphere or contact with skin. It should be noted
that EDX spectroscopy is particularly insensitive to carbon, strengthening
the conclusion that the material ejected from the injector is largely pure
and not contaminated by the ceramic used in the injector head or any other
source.
The EDX technique is performed in a Scanning Electron Microscope
(SEM), as part of the process high resolution images were taken of the crystal
surface. This provides useful information on the size of the particles that are
ablated from the injector, ideally the carbon would be produced in purely
ionised form, however in reality this is not the case and significant quantities
of neutral carbon are produced along with larger carbon fragments. Figure 2.9 shows one image of the surface and covers an area of approximately
23mm × 18mm. One large particle of carbon measuring about 100µm can be
seen in the lower half of the image. Particles of this size are likely to perturb
the plasma so that it may be necessary to include a fine mesh in front of
the injector to catch large particles such as these. Other than this and a
few other smaller particles the carbon deposition appears uniform, implying
that a significant quantity of the ablated material consists of particles on the
sub-micron scale and carbon ions.
2.4
2.4.1
Final design
The injector head
The spark head used for laboratory testing used small quantities of adhesive
to hold the carbon electrodes in place. This is not suitable for use in a
tokamak environment so the final design required that the components in
47
2.4 Final design
Figure 2.7: The current pulse for an 8KV 20nF discharge. The classic ringing
of a capacitor discharge can be seen as the current drops below zero and
recovers.
(a)
(b)
Figure 2.8: EDX spectrograms for beam energies of 10kV and 20kV showing
no significant contamination other than a small quantity of fluorine that is
likely due to external contamination
48
2.4 Final design
the spark head be held together mechanically. Aluminium oxide is also not
suitable for use in a tokamak so boron nitride was used as the insulator.
The electrodes and insulator were held in place by incorporating a series of
steps in their design, a pair of springs then holds the components in place,
see figures 2.10 and 2.11. Before installation on MAST the injector head
was cleaned and baked in vacuum for 24 hours to remove any contamination
caused during assembly. An image of the assembled head can be seen in
figure 2.13
A Langmuir probe was included in the head design and can be seen in
the top right corner of figure 2.10 and in closeup in figure 2.14. This probe
provides a Temperature/Density measurement close to the point of injection.
It also provides a good indication of the passing time of the strike point over
the DSF as the ion saturation current peaks as the strike point crosses the
Langmuir probe. The signal from the LP is recorded at 1MHz by the existing
Langmuir probe system on MAST.
The cables used to carry the electrical pulse were 311-KAP50 coaxial cable
supplied by Allectra. Coaxial cable was chosen as it was believed the outer
conductor would shield the vessel from electrical noise. The inner conductor
of this cable is just 0.45mm, although this is sufficient for transmitting the
electrical pulse it proved very fragile and made construction of the probe
head difficult. The cable is soldered to the copper contacts using flux-less
solder and this connection often broke when the head was being assembled.
It is likely that for future designs a larger, possibly non-coax wire will be
used.
Full manufacturing drawings of the injector head mounted on the DSF
can be seen in appendix A.
49
2.4 Final design
2.4.2
Power supplies and triggering
The electrical pulse that creates the spark is delivered by a bank of capacitors
located under the MAST vessel in a box installed for DSF specific equipment.
All the circuitry to charge and trigger the capacitor bank is contained in a
polycarbonate box that will be referred to as the Injector Power Supply or
IPS. This box is temporarily mounted in the permanent DSF box. Power
and signal cables installed in the DSF box are connected to the IPS. The
layout and operation of this box can be seen in drawings M115-02-101 and
M115-02-102 located in Appendix B.
The capacitor bank itself consists of 10 0.15µF polypropylene capacitors
mounted in parallel. The box electronics are powered by a Calex 24V DC
power supply. A Spellman MPS2.5kV10W24V HV power supply was used
for capacitor charging, this unit has a peak voltage of 2.5kV and a maximum
current of 4mA. An optical trigger signal is received from the MAST data
acquisition system and converted to a 5V electrical signal that is used to drive
an IXYS IGBT which triggers the capacitor discharge across the injector
electrodes. The IGBT (Insulated Gate Bipolar Transistor) is a power semiconductor device that combines an isolated gate FET and a bipolar power
transistor to achieve fast switching at high voltages and currents. As the
peak voltage used in the final design is 2.5kV a single IXGL75N250 2.5kV
IGBT was sufficient while during testing several of these were used in parallel
to switch voltages up to 5kV. The triggering circuit can be seen in appendix
B.
The HV power supply is regulated by a 0-5V signal from the MAST control system and returns the actual operating voltage via a 0-5V output signal.
Both these signals use isolation amplifiers to protect the MAST diagnostic
systems. A Bergoz CT-B0.05 current transformer is situated on the capacitor
50
2.5 Installation on MAST
bank output and provides a measure of the discharge current that is passed
to the MAST data acquisition system.
An optical enable signal is required for the HV supply to operate to avoid
the capacitors becoming accidentally charged when not mounted in the DSF
box. There is also an interlock on the IPS lid comprising of a normally closed
high voltage relay that is only opened when the 24V supply is on and the lid
is closed. If the 24V supply fails or the lid is opened the capacitors are then
discharged through a 300Ω resistor in a fraction of a second.
2.4.3
Modification after initial commissioning
During the first set of commissioning experiments in MAST campaign 8,
October 2011 the IGBT switch failed and was replaced so as to allow further
experiments. Although the cause of this was not known it is believed that it
was caused by a reverse voltage applied to the IGBT, possibly as the strike
point crossed the injector head in a beam heated discharge. The power
supplies were not disconnected from the injector head between experimental
sessions due to the difficult access during operations. To mitigate this risk
a transient suppression diode was added in parallel to the spark gap for the
second set of experiments in MAST campaign 9, June 2013.
2.5
Installation on MAST
The spark head was mounted in the head of the Divertor Science Facility
(DSF)[150], see figure 2.15. This system was developed on MAST to allow
samples and diagnostics easy access to the MAST divertor plasma in a similar
way to the DiMES system on DIII-D[156]. The DSF allows probes to be installed in the MAST divertor without venting the machine and is placed at a
51
2.5 Installation on MAST
radial location of 0.98m. Before installing the head it was cleaned and baked
for 24 hours to remove any contaminants from the manufacturing and assembly. The head was then installed on the DSF in a vacuum chamber isolated
from the MAST vessel by a gate valve. This process was completed in under
2 hours. Once this was done the vacuum chamber was pumped down using
an external rotary pump and a turbo-molecular pump to bring the pressure
to that inside the MAST vessel. Heating straps were then placed around
the chamber which was baked for several days to remove any contaminants
introduced in the installation process. The gate valve to the MAST vessel
was then opened and a pneumatic pump used to lift the DSF and injector
head into position in the MAST divertor. Figures 2.16 and 2.17 show the
injector head in its final location in the MAST divertor.
52
2.5 Installation on MAST
Figure 2.9: SEM image of carbon deposited on the surface of a quartz crystal
microbalance. Carbon particles up to 100µm can be seen, the overall width
of the image is approximately 20mm.
53
2.5 Installation on MAST
Figure 2.10: Close up of the injector head on top of the DSF probe. The
carbon electrodes, boron nitride insulators, copper contacts and the PEEK
support can all be seen as well as the integrated Langmuir probe.
54
2.5 Installation on MAST
Figure 2.11: Exploded view of the injector head on top of the DSF probe
showing the stepped construction allowing the components to be held in place
without the use of adhesives.
55
2.5 Installation on MAST
Figure 2.12: Cutaway view of the assembled injector head.
Figure 2.13: Image of the injector head prior to installation on MAST.
56
2.5 Installation on MAST
Figure 2.14: Cutaway view of the assembled injector head showing the integrated Langmuir probe.
57
2.5 Installation on MAST
Figure 2.15: Schematic overview drawing of the DSF showing the insertion
system and the independent pumping system. The drawing shows the DSF
configuration when the head is fully inserted into the machine
58
2.5 Installation on MAST
Figure 2.16: Cutaway of dummy injector head in place in the MAST divertor.
Figure 2.17: Schematic of the the installed injector head seen from above.
59
CHAPTER
3
Experimental method and data
3.1
3.1.1
Experimental approach
First use
Commissioning of the injector was carried out on MAST during September
2011. Images of impurity injection were subsequently taken in two sets of
experiments, once in October 2011 during campaign 8 and then again in
June 2013 during campaign 9. The data used for comparison with simulation
was from the second set of experiments, however a brief description of the
commissioning process and initial experiments and is included in appendix
C.
60
3.1 Experimental approach
3.1.2
Diagnostics
In order to make useful comparisons of impurity transport between modelling and experiment it is important to accurately characterise the background plasma. This is particularly true when using the Onion Skin Method
(see 1.4.5). Langmuir probes positioned in the MAST divertor[157] and a
mid-plane Thomson scattering system[158, 159] provide electron density and
temperature data that forms the basis for the OSM reconstruction of the
background plasma. These diagnostics are available routinely on MAST.
The goal of the experiments was to image injected carbon at different
points relative to the outer strike point from a few centimetres into the private
flux region to a few centimetres into the outer SOL. This is achieved by
varying the timing of the injection as the strike points sweep across the
targets. An initial guess of the location of the strike point relative to the
DSF at a given time was made using EFIT [160] equilibrium construction.
This was then compared with data from the Langmuir probe mounted on the
injector head and with data from the divertor Langmuir probes. There are
often discrepancies between the values obtained from EFIT and those from
the Langmuir probes, this will be discussed on a shot by shot basis where
appropriate.
The primary diagnostic requirement for this experiment is for the fast
visible cameras positioned in sectors 1 and 11 of the MAST vessel, see figures
3.1 and 3.2. Photron Ultima APX-RS cameras were used at both locations.
A significant part of the experimental process was concerned with obtaining
the highest temporal resolution possible. Taking the plasma sound speed
(equation 1.1) as an estimate for the ion velocity using typical near target
temperatures of Ti = Te = 25ev gives cs ≈ 5x104 ms−1 . An ion moving at
this speed would take 50µs to travel 10cm, frame rates better than this are
61
3.1 Experimental approach
therefore required to resolve the formation and transport of the plume. In
order to achieve a strong signal the standard 50mm lenses on the fast cameras
was replaced by a 25mm lens that reduced both the field of view and the
spatial resolution by a factor of 2 but allowed shorter integration times so
that the cameras could be run at 75kHz-100kHz, giving a time between
frames of 10 − 13µs.
Band-pass filters were used to select the carbon II and carbon III lines
emitted by the ablated carbon as it is ionised within the SOL. The carbon
II filter on sector 1 had a bandwidth of 2.76nm centred around 514.91nm
and the carbon II filter on sector 11 had a bandwidth of 2.75nm centred on
514.79nm, although the primary emission of the carbon II multiplet is centred
at 514nm this wavelength is within the range of both filters. The carbon III
filter had a bandwidth of 1.42nm centred around 465.29nm, encompassing
the carbon III multiplet also centred around 465nm. Filters for the Dα line at
656.1nm and CI line at 910nm were also fitted to the cameras on a remotely
changeable carousel. In order to achieve a strong signal the standard 50mm
lenses on the fast cameras was replaced by a 25mm lens that reduced both
the field of view and the spatial resolution by a factor 2 but allowed shorter
integration times so that the cameras could be run at 75kHz-100kHz, giving
a time between frames of 10 − 13µs.
Having access to two cameras at different positions allowed the choice of
either running the same filters on both cameras or to run two different filters.
Using the same filters provides tighter constraints on the plume dynamics for
a single charge state. This was restricted to the carbon II line as carbon III
filters were not available for both cameras. In addition the carbon II emission
was generally too weak to show the plume evolution. Using two different
filters has the obvious advantage of showing the evolution of the ionisation
62
3.1 Experimental approach
Figure 3.1: View of the DSF from the fast camera situated at a view port in
sector 1 of MAST
Figure 3.2: View of the DSF from the fast camera situated at a view port in
sector 11 of MAST
63
3.2 Experimental data
states of the injected carbon providing additional modelling constraints.
Flow data was also available for some of the experimental sessions, this
was provided by a coherence imaging diagnostic (see 1.3.1) using the carbon
III emission line[1]. The MAST instrument operates with each pixel corresponding to 1.5mm in the plasma cross-section with a vertical resolution of
approximately 12 pixels. This diagnostic produces a 2D map of line averaged
flow with a temporal resolution of 1ms and a flow resolution of approximately
1km/s.
3.2
Experimental data
Although useful data was obtained during the first experimental sessions
detailed analysis and simulation was not performed before the opportunity
of a further set of experiments in June 2013. As MAST was due to begin
a shutdown for the upgrade to the super-X divertor this would be the last
possibility for experiment over the timescale of this project. No external
heating was used in the initial experiments due to the risk of damage to the
injector system. The temperature and density of the plasma was therefore
relatively low and the relevance to future devices limited. The data shown
here was taken during an experimental session using beam heated plasmas
on Thursday 20th June 2013.
3.2.1
Plasma configuration
Two plasma configurations were used in the final experimental session. A
single beam heated L-mode plasma based on reference 28787 and a 2 beam
heated ELM-free H-mode plasma based on reference 28982. An ELM-free Hmode was chosen so as to avoid the complexities in both measurement and
64
3.2 Experimental data
simulation introduced by the ELMS. The strike point in the reference H-mode
shot did not cross the injection location, the P2 and solenoid coil current were
increased to move the strike point and allow injection into the outer SOL
although not at the strike point itself. At the injection times the L-mode
plasmas parameters were Ip ≈ 900M A, BT ≈ 0.55T , ne ≈ 13 × 1019 m−2
and PN BI = 1.8M W where PN BI is the total power from Neutral Beam
Injection (NBI). The H-mode parameters were Ip ≈ 900M A, BT ≈ 0.55T ,
ne ≈ 25 × 1019 m−2 and PN BI = 3.5M W . In total data was taken for 6
shots, table 3.1 shows the injection timing, strike point position given by
EFIT, the distance between the injection location and the strike point and
the camera filters used for each shot. For the L-mode shots a charging voltage
of 1.5kV was used, equating to a stored energy of 1.7J, for the H-mode shots
only limited emission was seen at this voltage so it was increased to 2.4kV ,
equating to a stored energy of 4.3J.
Shot
tspark
Strike point
∆R
Sector 1
Sector 11
(ms)
position (m)
(cm)
filter
filter
29125 - L-mode
250
0.981
0.4
Carbon II
Carbon II
29126 - L-mode
250
0.976
0.9
Carbon II
Carbon II
29128 - L-mode
240
0.971
1.4
Carbon I
Carbon III
29129 - L-mode
240
0.973
1.2
Carbon I
Carbon III
29139 - H-mode
320
0.985
0.0
Carbon II
Carbon II
29142 - H-mode
320
0.989
-0.4
Carbon I
Carbon III
Table 3.1: Shots from the final experimental session
For reference time traces for Dα emission, plasma current, neutral beam
total injected power, line integrated density and toroidal magnetic field on
the magnetic axis for the L-mode and H-mode shots can be seen in figures 3.3
65
3.2 Experimental data
Figure 3.3: Dα emission, plasma current, neutral beam total injected power,
line integrated density and toroidal magnetic field on the magnetic axis for
the L-mode shots 29125, 29126, 29128 and 29129. The impurity injection
times are denoted by dashed vertical black lines.
and 3.4. The line integrated density data was not available for shot 29139.
3.2.2
Injection duration
It can reasonably be assumed that ion and neutral injection occurs predominantly while current is flowing across the spark gap from the capacitor bank.
The measured current leaving the capacitor bank for the 6 shots of interest can be seen in figure 3.5. The current can be seen to oscillate or ’ring’
as is expected from a capacitor discharge. The width of the initial positive
current surge is approximately 10µs while the ringing continues for 40µs for
the L-mode shots and 60µs for the H-mode shot, which used a higher charg-
66
3.2 Experimental data
Figure 3.4: Dα emission, plasma current, neutral beam total injected power,
line integrated density and toroidal magnetic field on the magnetic axis for
the H-mode shots 29139 and 29142. The impurity injection time is denoted
by a dashed vertical black line.
67
3.2 Experimental data
ing voltage (see 3.2.1). An estimate for the injection duration can also be
obtained from the CCD imaging, figure 3.6 shows the time evolution of the
emission observed by the CCD at the point of injection. Although there is a
large degree of uncertainty in this method the duration of the high emission
peaks support the view that the injection occurs over the duration of the
ringing cycle and not just during the initial current surge or significantly
after the discharge has ended. A further inaccuracy arises due to the capacitance of the transmission line from the power supplies to the injector head.
Charge may build up in the coaxial cables which can then discharge across
the spark gap at a later time.
3.2.3
Injection location
Identifying the injection location relative to the strikepoint is very important
when comparing experiments with simulation. For the L-mode shot injection
was performed at 2 locations, due to the limited experimental time available
only 1 injection location was performed for the H-mode shot. Analysis is
presented for the three locations. Figures 3.7, 3.8 and 3.9 each show the
strike point location calculated from EFIT, data from the divertor Langmuir
probes and data from the injector Langmuir probe for the three injection
locations.
Plasma perturbation
The on-board Langmuir probe provides a means of estimating the perturbation to the plasma at the targets caused by the injection. The LP ran at a
frame rate of 6.5 × 10−5 s, approximately 15kHz longer than the spark duration however any significant effect would likely be visible in the data. Figure
3.10 shows the measured saturation current against time for the 6 shots of
68
3.2 Experimental data
(a) 29125 & 29129
(b) 29126 & 29128
(c) 29139 & 29142
Figure 3.5: Injector discharge current measure by the integrated current
transformer. The solid lines show the current from the first shot in each plot
while the dashed line the second.
69
3.2 Experimental data
(a) 29125
(b) 29126
(c) 29139
Figure 3.6: Maximum carbon II emission observed within 5 pixels of the
injection location for the three shots 29125, 29126 and 29139. This provides
an estimate of the duration of carbon injection of approximately 40µs for the
L-mode cases and 60µs for the H-mode case.
70
3.2 Experimental data
(a) EFIT
(b) Divertor LPs
(c) Injector LP
Figure 3.7: EFIT and LP data from shot 29125 showing the strike point
position at the injection time of 250ms. a) Strike point location plotted
against time shows the strike point moving outwards until it crosses the
injector head then moves inwards again. b) Radial density profile from the
divertor Langmuir probes, the strike point lies close to the peak of this profile.
c) Saturation current from the on-board Langmuir probe plotted against time
showing an increase just before the injections time as the strike point crosses
the injector.
71
3.2 Experimental data
(a) EFIT
(b) Divertor LPs
(c) Injector LP
Figure 3.8: EFIT and LP data from shot 29126 showing the strike point
position at the injection time of 240ms. a) Strike point location plotted
against time shows the strike point moving outwards until it crosses the
injector head then moves inwards again. b) Radial density profile from the
divertor Langmuir probes, the strike point lies close to the peak of this profile.
c) Saturation current from the on-board Langmuir probe plotted against time
showing an increase just before the injections time as the strike point crosses
the injector.
72
3.2 Experimental data
(a) EFIT
(b) Divertor LPs
(c) Injector LP
Figure 3.9: EFIT and LP data from shot 29139 showing the strike point
position at the injection time of 320ms. a) Strike point location plotted
against time shows the strike point moving outwards until it crosses the
injector head then moves inwards again. b) Radial density profile from the
divertor Langmuir probes, the strike point lies close to the peak of this profile.
c) Saturation current from the on-board Langmuir probe plotted against time
showing an increase just before the injections time as the strike point crosses
the injector.
73
3.2 Experimental data
interest. It can be seen that there is no evidence for significant perturbation
of the background plasma.
3.2.4
Electron temperature and density data
Target data
Langmuir probes are installed on both the upper and lower divertor on
MAST. For the six shots of interest strike point data was only available
from the outer divertor arrays. In the case of the upper inner divertor probes
the amplifier used to drive the probes was used to drive the probe on the
injector head. For the lower inner divertor the strike point was too high to
register on the probes at the time of the injection. For shot 29139 no Langmuir probe data exists however shot 29142 was a repeat of this shot so the
data taken in 29142 is used for simulation of 29139. Data for shots 29125,
29126 and 29139/29142 can be seen in figures 3.11, 3.12 and 3.13.
A spline fit to the data has also been plotted over the raw data. This
fit was used as input for simulation, see section 5.2.2. The data has been
averaged over 3 timeslices from centre on the injection time. The lower target
data for shot 29139 has also been shifted radially so that the density peak
aligns with the strike point location calculated by EFIT as there is significant
error in the EFIT reconstruction. For the L-mode shot 29126 and H-mode
shot 29139 the upper divertor temperature data appears to be purely noise,
this data has been fixed at an value of 6eV. The initial data can be seen
as crosses on all plots. In the presence of magnetic fields Langmuir probes
are sensitive to the angle of incidence of the field, this has been accounted
for simplistically by using the projected area of the Langmuir probes with
respect to the incident magnetic field.
74
3.2 Experimental data
(a) 29125
(b) 29126
(c) 29139
(d) 29129
(e) 29129
(f) 29142
Figure 3.10: Saturation current plotted against time taken from the on-board
Langmuir probe. There is no discernible perturbation seen at the injection
time for each shot, shown by a dashed vertical line.
75
9 1e18
16
8
14
7
Electron temperature (eV)
Electron density (m−3 )
3.2 Experimental data
6
5
4
3
2
12
10
8
6
4
2
1
0
0.95
1.05
1.15
ψn
1.25
0
0.95
1.35
EFIT strike point
1.05
1.15
1.25
1.05
1.15
ψn
1.35
1.8 1e18
18
1.6
16
1.4
14
Electron temperature (eV)
Electron density (m−3 )
(a) Upper divertor
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.95
12
10
8
6
4
2
1.05
1.15
ψn
1.25
1.35
0
0.95
EFIT strike point
ψn
1.25
1.35
(b) Lower divertor
Figure 3.11: Outer target electron density and temperature data against
normalised poloidal flux for L-mode shot 29125. The measured data is represented by crosses and the data used in simulation by the solid line.
76
8 1e18
16
7
14
Electron temperature (eV)
Electron density (m−3 )
3.2 Experimental data
6
5
4
3
2
12
10
8
6
4
1
0
0.95
2
1.05
1.15
ψn
1.25
0
0.95
1.35
EFIT strike point
1.05
1.15
1.25
1.05
1.15
ψn
1.35
1.8 1e18
16
1.6
14
1.4
Electron temperature (eV)
Electron density (m−3 )
(a) Upper divertor
1.2
1.0
0.8
0.6
0.4
10
8
6
4
2
0.2
0.0
0.95
12
1.05
1.15
ψn
1.25
1.35
0
0.95
EFIT strike point
ψn
1.25
1.35
(b) Lower divertor
Figure 3.12: Outer target electron density and temperature data against
normalised poloidal flux for L-mode shot 29126.The measured data is represented by crosses and the data used in simulation by the solid line.
77
8 1e18
16
7
14
Electron temperature (eV)
Electron density (m−3 )
3.2 Experimental data
6
5
4
3
2
12
10
8
6
4
1
0
0.95
2
1.05
1.15
ψn
1.25
0
0.95
1.35
EFIT strike point
1.05
1.15
ψn
1.25
1.35
1.25
1.35
1.8 1e18
16
1.6
14
1.4
Electron temperature (eV)
Electron density (m−3 )
(a) Upper divertor
1.2
1.0
0.8
0.6
0.4
10
8
6
4
2
0.2
0.0
0.95
12
1.05
1.15
ψn
1.25
1.35
0
0.95
EFIT strike point
1.05
1.15
ψn
(b) Lower divertor
Figure 3.13: Outer target electron density and temperature data against
normalised poloidal flux for H-mode shot 29139. The measured data is represented by crosses and the data used in simulation by the solid line.
78
3.2 Experimental data
Midplane data
The Thomson scattering system on MAST was operated in burst mode,
whereby 8 measurements are taken 500µs apart over a 3.5ms interval giving
improved diagnostic coverage at the time in question. This also provides a
measure of the potential perturbation caused by the injection. No significant
difference was observed in the density or temperature signals after the injection, showing that any perturbation caused by the injection was not large
enough to propagate upstream as far as the midplane. Figure 3.14 show the
density and temperature data for shots 29125, and 29139 averaged over the
5 time slices. Spline fits are included as for the target data. Data from the
low field side and high field side were overlayed before averaging. Ideally
one would use the respective data from the low and high field sides, however
the noise on the low field side data made this data unusable for modelling
purposes.
3.2.5
Flow data
Flow data taken from the coherence imaging diagnostic (see section 1.3.1)
can be seen for shots 29125, 29126 and 29139 in figure 3.15. The measured
flow values are line averaged along the line of sight of the diagnostic. The
data seen here is projected from the image plane onto the R,Z plane where
the line of sight is tangential to the toroidal magnetic field and do not take
into account either the field line angle or the distribution of flow along the
line of sight. However the principle contribution to the average flow is from
the tangential component of the line of sight, so that the values serve as
a useful guide for comparison with simulation. This data will be discussed
further in section 5.2.3.
79
3.2 Experimental data
2.5 1e19
300
250
Electron temperature (eV)
Electron density (m−3 )
2.0
200
1.5
1.0
0.5
150
100
50
LCFS
0.0
0.6
0.7
0.8
0.9
ψn
1.0
1.1
0
0.6
1.2
0.7
0.8
0.9
ψn
1.0
1.1
1.2
6 1e19
600
5
500
Electron temperature (eV)
Electron density (m−3 )
(a) Shot 29125
4
400
3
2
300
200
1
100
LCFS
0
0.6
0.7
0.8
ψn
0.9
1.0
1.1
0
0.6
0.7
0.8
ψn
0.9
1.0
1.1
(b) Shot 29139
Figure 3.14: Midplane electron density and temperature data for shot 29125
and 29139 against normalised poloidal flux. Data from the high and low field
sides have been combined.
80
3.2 Experimental data
(a) 29125
(b) 29126
(c) 29139
Figure 3.15: Flow data taken using the coherence imaging diagnostic measuring carbon III emission [1].
81
CHAPTER
4
Image processing and analysis
4.1
Acquired CCD data
The data from the filtered fast cameras is the principle diagnostic data resulting from the injection experiments. Figures 4.1 and 4.2 show unprocessed
images from both sectors showing the camera view and an example of injection respectively. Although these shots are from the first set of experimental
sessions and will not be discussed further they are useful as an example of
the raw data taken by the cameras.
For shots 29125 to 29142 the camera on sector 1 ran with a frame rate
of 75kHz while the camera on sector 11 ran at 100kHz. Both cameras
integrated over the full duty cycle with integration times 13.3µs and 10.0µs
respectively. The remainder of this section will discuss the images taken and
the processing applied to each image for shots 29125, 29126, 29128, 29129,
82
4.1 Acquired CCD data
(a) Sector 1
(b) Sector 11
Figure 4.1: Unfiltered images from both sectors showing the actual camera
views.
(a) Sector 1
(b) Sector 11
Figure 4.2: Unprocessed images from both sectors showing CII filtered images
from shot 27075. Injection location 4cm into the private flux zone with an
integration time of 33µs.
83
4.2 Magnetic field projection
29139 and 29142.
4.1.1
Camera Calibration
Only one of the Photron cameras used for the imaging was calibrated in the
laboratory, it is assumed that the other camera, of identical make, has the
same sensitivity. Although this is unlikely to be strictly true there is a high
level of error inherent in the calibration, making this assumption valid within
errors. Calibration was performed in a laboratory environment using a light
source with a set luminance of 24.723kcd/m2 . The calibration images and
a horizontal slice of the calibration coefficients for the carbon II, carbon III
and Dα filters can be seen in figure 4.3, no calibration data was taken for the
carbon I filter.
4.2
Magnetic field projection
The goal of this thesis is to compare the parallel transport of impurities
with simulation. This is quantified by projecting the magnetic field onto the
images taken and measuring the emission along the projected field line. It
is assumed that transport along the field line dominates so that the injected
carbon remains bound to the field line and any observed emission originates
from that field line. This can then be compared to the emission from the
relevant flux tube in the simulation.
4.2.1
Camera registration and field line projection
In order to accurately project the magnetic field onto the captured images
it is necessary to accurately know the 2 dimensional magnetic field and the
position and optical characteristics of the cameras. The magnetic field is
84
4.2 Magnetic field projection
(a) CII
(b) CII
(c) CIII
(d) CIII
(e) Dα
(f) Dα
Figure 4.3: Calibration curves for the carbon II, carbon III and Dα filters.
85
4.2 Magnetic field projection
Parameter
Sector 1
Sector 11
no x pixels
96
128
no y pixels
128
64
x centre
48.5
64
y centre
64.5
128
focal length
5.8mm
5.5mm
x position
0.68m
-1.47m
y position
2.21m
1.50m
z position
-1.18m
-1.34m
pitch
30.6◦
-51.45◦
roll
-112.5◦
-109.0◦
yaw
170.9◦
-164.0◦
pixel size
17µm
17µm
Table 4.1: Camera registration
obtained from EFIT, while the camera position must be calculated using
software available on MAST. Camera images are compared to wire-frame
models of the MAST vessel and matching pixels are manually indicated on
the image and the model. The software then performs a minimisation on the
variable parameters of the system. The calculated parameters can be seen for
both cameras in table 4.1. The locations given in table 4.1 result in a spatial
resolution at the point of injection of 5.1mm/pixel for the sector 1 camera
and 4.5mm/pixel for the sector 11 camera. At the furthest visible extent of
the plume the resolution becomes 6.2mm/pixel for the sector 1 camera and
7.8mm/pixel for the sector 11 camera.
In order to project field lines onto the camera images it is necessary to
first calculate the path of the field line. This is done using a fourth order
86
4.3 Image processing
Runge-Kutta method described here.
P0 = (R, Z, Φ)
δxB0
k1 = P0 +
2 × |B|
δxB1
k 2 = k1 +
2 × |B|
δxB2
k 3 = k2 +
2 × |B|
1
Pi+1 = Pi + (k1 + 2k2 + 2k3 + k4 )
6
(4.1)
(4.2)
(4.3)
(4.4)
(4.5)
The field line is followed in both directions from a given starting point providing a set of points in 3 dimensions. These points are then projected onto
the image plane of the camera to give the final projection.
4.3
Image processing
In order to clearly identify the injected plume the plasma background must
be subtracted from the images of the injection. This is done using the frame
immediately before the injection and results in a clearly defined plumes.
A contour map is used to show the relative emission intensity from each
plume in successive frames after the injection. Figures 4.4 to 4.15 show these
background subtracted images filtered to the carbon II emission line for both
sectors. Magnetic field lines have been projected onto the image, the first of
these originates at the injection location, while further field lines are added
at regular intervals of poloidal angle in order to aid the visual interpretation
of the images. In the case of shot 29125 significant emission in the frame
taken at the injection time appears at a different location to the centre of
the DSF. This appears to be approximately 2cm above the top of the injector
head and so the projected field line is taken to originate at this point. This is
87
4.3 Image processing
likely due to neutral carbon being injected upwards until it is ionised by the
hot plasma close to the separatrix and provides evidence that the injection
location was inside the outer strike point for this shot and, not on the strike
point as indicated by EFIT and the divertor Langmuir probes (see 3.2.3).
For shots 29126 and 29139 the initial emission appears close to the centre of
the DSF so the projected field line is originated at this point.
4.3.1
CII emission
For shots 29125, 29126 and 29139 carbon II filters were used on both cameras.
Figures 4.4 to 4.9 show calibrated emission from each of these cameras as
well as projections of the magnetic field lines originating at the divertor to
aid in visualisation.
4.3.2
CI and CIII emission
For shots 29128, 29128 and 29142 a carbon I filter at 910nm was used on the
sector 1 camera and a carbon III filter at 465nm was used on the sector 11
camera. Background subtracted images of these shots can be seen in figures
4.10 to 4.15 along with field line projections as in the previous images. None
of the images taken using carbon III filters on sector 11 show significant
emission aligned with the magnetic field apart from at the injection location,
however the full set of images has been included for completeness. Some
emission can be seen in the sector 1 view of H-mode shot 29142 using a CIII
filter, however this emission is only just detectable by the camera and only
just above the level of noise. It should be noted that for this shot the highest
charging voltage of 2.4kV was used and as an H-mode plasma conditions are
hotter than in the 2 L-mode shots. Similarly no significant CI emission was
observed for the sector 1 views using CI filters apart from at the injection
88
4.3 Image processing
Figure 4.4: Contour plots of the carbon plumes from L-mode pulse 29125
imaged from sector 1 using a CII filter at 515nm. The images are each
separated by 13µs. Magnetic field lines originating at the injection radius
can be seen projected onto the image.
89
4.3 Image processing
Figure 4.5: Contour plots of the carbon plumes from L-mode pulse 29125
imaged from sector 11 using a CII filter at 515nm. The images are each
separated by 13µs. Magnetic field lines originating at the injection radius
can be seen projected onto the image.
90
4.3 Image processing
Figure 4.6: Contour plots of the carbon plumes from L-mode pulse 29126
imaged from sector 1 using a CII filter at 515nm. The images are each
separated by 13µs. Magnetic field lines originating at the injection radius
can be seen projected onto the image.
91
4.3 Image processing
Figure 4.7: Contour plots of the carbon plumes from L-mode pulse 29126
imaged from sector 11 using a CII filter at 515nm. The images are each
separated by 10µs. Magnetic field lines originating at the injection radius
can be seen projected onto the image.
92
4.3 Image processing
Figure 4.8: Contour plots of the carbon plumes from H-mode pulse 29139
imaged from sector 1 using a CII filter at 515nm. The images are each
separated by 13µs. Magnetic field lines originating at the injection radius
can be seen projected onto the image.
93
4.3 Image processing
Figure 4.9: Contour plots of the carbon plumes from H-mode pulse 29139
imaged from sector 11 using a CII filter at 515nm. The images are each
separated by 10µs. Magnetic field lines originating at the injection radius
can be seen projected onto the image.
94
4.4 Emission parallel to the magnetic field
Figure 4.10: Contour plots of the carbon plumes from L-mode pulse 29128
imaged from sector 1 using a CI filter at 910nm. The images are each separated by 13µs. Magnetic field lines originating at the injection radius can
be seen projected onto the image.
location. This is likely due to the carbon quickly ionising once in contact
with the plasma.
4.4
Emission parallel to the magnetic field
A measure of the parallel transport of the injected carbon is obtained by
reading the emission from the images (see 4.3) along the path of the projected
95
4.4 Emission parallel to the magnetic field
Figure 4.11: Contour plots of the carbon plumes from L-mode pulse 29128
imaged from sector 11 using a CIII filter at 465nm. The images are each
separated by 10µs. Magnetic field lines originating at the injection radius
can be seen projected onto the image.
96
4.4 Emission parallel to the magnetic field
Figure 4.12: Contour plots of the carbon plumes from L-mode pulse 29129
imaged from sector 1 using a CI filter at 910nm. The images are each separated by 13µs. Magnetic field lines originating at the injection radius can
be seen projected onto the image.
97
4.4 Emission parallel to the magnetic field
Figure 4.13: Contour plots of the carbon plumes from L-mode pulse 29129
imaged from sector 11 using a CIII filter at 465nm. The images are each
separated by 10µs. Magnetic field lines originating at the injection radius
can be seen projected onto the image.
98
4.4 Emission parallel to the magnetic field
Figure 4.14: Contour plots of the carbon plumes from H-mode pulse 29142
imaged from sector 1 using a CI filter at 910nm. The images are each separated by 13µs. Magnetic field lines originating at the injection radius can
be seen projected onto the image.
99
4.4 Emission parallel to the magnetic field
Figure 4.15: Contour plots of the carbon plumes from H-mode pulse 29142
imaged from sector 11 using a CIII filter at 465nm. The images are each
separated by 10µs. Magnetic field lines originating at the injection radius
can be seen projected onto the image.
100
4.5 Repeat injection
field starting at the injection location. The images are first smoothed over 2
pixels using the IDL Gaussian smoothing algorithm. This reduces the noise
without significantly affecting the absolute measured emission. This line
integrated emission along the projected magnetic field can be seen in figures
4.16, 4.17 and 4.18. This is compared to results obtained from simulation in
section 5.4. The data from the H-mode shot 29139 shows a clear expansion
along the field line and an estimate of the impurity parallel velocity can be
made of 14 ± 3ms−1 .
4.5
Repeat injection
In several cases a second discharge occurred after 60µs. Examples of this
can be seen in figure 4.19. In the frame immediately preceding the second
discharge the visible plumes were at the lower limit of sensitivity of the
CCDs, indicating that the following frame would not have provided further
significant information on transport. Due to this, and considering the added
complexity of modelling a second impurity injection while impurities were
still present in the plasma data from the injection due to the second discharge
will not be used for comparison with simulation. This second discharge did
not occur during the initial set of experiments and it is possible that a change
to the charge carrying cable in the vacuum system from coaxial to single core
increased the inductance of the system and caused a second delayed current
pulse. This change was made for reasons of mechanical reliability and could
potentially be reversed if suitable coaxial cable were used.
101
4.5 Repeat injection
(a) Sector 1
(b) Sector 11
Figure 4.16: CII emission intensity along the field line from sectors 1 (a) and
11 (b) for shot 29125
102
4.5 Repeat injection
(a) Sector 1
(b) Sector 11
Figure 4.17: CII emission intensity along the field line from sectors 1 (a) and
11 (b) for shot 29126
103
4.5 Repeat injection
(a) Sector 1
(b) Sector 11
Figure 4.18: CII emission intensity along the field line from sectors 1 (a) and
11 (b) for shot 29139
104
4.5 Repeat injection
(a) 29126
(b) 29139
Figure 4.19: Secondary injection. CII filtered images taken from shot 29126
(a) and shot 29139 (b) showing the initial injection in the first frame and a
secondary burst of carbon in frames 7 and 5 respectively.
105
CHAPTER
5
DIVIMP Simulation
5.1
OSM-EIRENE-DIVIMP
The data obtained from experiment was compared with simulation using the
OSM-EIRENE-DIVIMP set of codes see 1.4.7. This package is currently
being used in ITER modelling, the results of which are used being used to
guide the ITER design. OSM (see 1.4.5) simulates the hydrogenic background plasma by solving a set of 1D fluid equations parallel to the magnetic
field, EIRENE provides the neutral dynamics and DIVIMP uses a MonteCarlo method to follow impurity particles on the plasma background.
5.1.1
OSM
As described in section 1.4.5 OSM performs interpretive modelling of the
plasma SOL, in that the goal is to provide as complete a description of
106
5.1 OSM-EIRENE-DIVIMP
the SOL given the available experimental data. The code provides a number of different methods for creating the independent 1D plasma solutions
along each flux tube, all tailored towards certain plasma conditions. The
method used here is SOL option 28, also used in current ITER simulations.
This method is not currently included in the DIVIMP documentation[161]
although has previously been used to simulate DIII-D plasmas[162].
A reconstruction of the magnetic equilibrium from a code such as EFIT is
used to create a grid containing a series of tubes of constant flux, see figure
1.2. Each flux tube is then split into an upper and lower section by prescribing a ’symmetry’ point approximately halfway between the upper and
lower targets. The temperature along each half tube is then prescribed by
interpolating from data at the targets to data at the symmetry point and
assuming Te = Ti . For this case a 7/2 power law was used, based on the
assumption that the parallel transport is conduction dominated. This temperature profile is then used to solve the mass and momentum conservation
equations
d
(ni vi ) = Sparticle + Aparticle
ds
(5.1)
d
(Te + Ti + mi ni vi2 ) = Smomentum + Amomentum
ds
(5.2)
where s is the distance along the flux tube and the final term in each case is
an anomalous source that effectively includes any physics not included in the
model used here, such as cross-field transport, particle drifts or turbulence.
The anomalous source is defined as a function of s by the user and the
coefficients calculated by the OSM solver, in this case it is set to the simplest
case of a constant along s. This approach allows each flux tube to be treated
independently, there is no perpendicular transport, either diffusive, advective
107
5.1 OSM-EIRENE-DIVIMP
or turbulent, between two neighbouring tubes.
5.1.2
EIRENE
The EIRENE code is widely used in the fusion community to simulate the
behaviour and plasma interaction of neutral particles and radiation in tokamaks. The plasma solution produced by OSM is dependent on the interaction
of the plasma with neutrals and conversely the neutral population is dependent on the plasma solution. The neutral particles are not confined by the
magnetic fields present in the tokamak and therefore interact with all regions
of the SOL. This results in particle, energy and momentum sources over a
large extent of the plasma. EIRENE uses the plasma solution calculated by
OSM to calculate the neutral solution and returns this to OSM. This process
is then repeated until a steady state solution is reached, although in practice
this is often achieved after just a few iterations. Although EIRENE has 3D
capability only a 2D solution is required when used with OSM.
5.1.3
DIVIMP
Although DIVIMP is essentially a stand alone code the version used here
controls the running of OSM and EIRENE and the creation of the background
plasma solution. The process of obtaining simulations of impurity behaviour
begins with the simulation of the background plasma, which is usually first
calculated without impurities. This solution is then saved to file and used by
DIVIMP when simulating the impurity behaviour. Impurities are injected
at a location defined by the user, the impurities are then followed using a
Monte-Carlo method until a steady state is reached. It is possible to set a
maximum dwell time for the particles launched by DIVIMP so that after a
set time they are not followed and remain in the position they occupied after
108
5.1 OSM-EIRENE-DIVIMP
the dwell time is reached. This allows a time dependent process, such as
the injection of impurities, to be simulated up to the time that the injection
ceases. DIVIMP uses the the ADAS atomic and molecular database [163] for
all atomic processes.
Parallel transport is modelled by calculating the forces on the impurity
particles from equation 1.11 as well as parallel diffusion. DIVIMP includes
several different options for applying these forces, the setup used in this case
is now described.
The first term in equation 1.11, the force due to the electric field does
not need elaboration. The stopping time (τs ) in the friction term is given by
r
τs = mi Tb
1.0
Tb
×
mb
mb
2 2
4
6.8 × 10 1.0 + mi Nb Zb Zi λ
(5.3)
where the subscript b refers to values for the background plasma and λ is
the mean free path for the impurity ions. The electron and ion temperature
gradient force coefficients αe and βi are given by
αe =
0.71Zi2 , βi
√
1 − µ − 5Zi2 µ 2µ (1.1µ − 0.35)
= −3
(2.6 − 2µ + 5.4µ2 )
(5.4)
where
µ=
mi
mi + mb
(5.5)
the calculation of collisional diffusive transport uses a parallel time constant (τk ) given by
r
τk = mi
Tb
Ti
×
mb
6.8 × 104 1.0 +
mb
mi
Nb Zb2 Zi2 λ
(5.6)
Perpendicular transport is included by setting a perpendicular diffusion
coefficient D⊥ to an empirical value, in this case the commonly adopted value
109
5.2 Plasma solution
of 1m2 s−1 [164]. No terms for advective transport exist in DIVIMP. Particle
drifts that can result in cross field transport are also not present, as stated
in section 1.4.7.
5.2
Plasma solution
Obtaining a reliable plasma solution from OSM relies heavily on having detailed diagnostic data for the plasma to be simulated. The solution is based
on 2 sets of observations, those from plasma diagnostics providing temperature, density and other kinetic information and observations that provide the
magnetic grid on which the simulation is run. As has been noted in section
1.5 the MAST tokamak has a comprehensive array of diagnostics that make
it very suitable for simulation using OSM. The plasma diagnostic data used
as input to these simulations is detailed in chapter 3. DIVIMP allows the
plasma solution to be stored so that ions can be injected into the simulation
without having to recalculate. For these cases a total of 4 OSM-EIRENE iterations were required to achieve a steady state, at which point no significant
change is seen with further iterations.
5.2.1
Simulation Equilibrium
The grids that define the geometry of the simulations were initially obtained
from eqdsk files produced by the EFIT code, the lower divertor sections of
these grids can be seen in figure 5.1.
A simple check on the validity of the calculated equilibrium can be made
by comparing the strike point location given by the reconstruction with kinetic data from the divertor Langmuir probes. Figures 3.7, 3.8 and 3.9 show
the EFIT calculated strike point position, divertor Langmuir probe density
110
5.2 Plasma solution
(a) 29125
(b) 29126
(c) 29139
Figure 5.1: Grids used for the impurity injection simulation. These are
produced using EFIT magnetic equilibrium reconstruction.
111
5.2 Plasma solution
data and injector Langmuir probe data for shots 29125, 29126 and 29139. It
is expected that the density maximum be close to the strike point location,
which is the case for the shots 29125 and 29126, however for shot 29125 this
data is contradicted by the injector mounted Langmuir probe, which suggests that the the strike point may have already passed over the injector.
This is consistent with the imaging of injection for 29125, which suggests
that the injection took place inside the outer strikepoint. For shot 29139 the
Langmuir probe data suggests that the strike point location calculated by
EFIT is inboard of the actual location, the density peak is significantly inside the calculated strikepoint and there is no increase in saturation current
seen on the injector Langmuir probe at the time of the shot, which would
be expected as the strike point passes over the probe. In order to account
for the clear discrepancy in the strike point position identified by EFIT the
injection location used in the simulation was altered to account for this: this
is described in sections 5.3.1 and 5.5.2.
5.2.2
Background plasma simulation
The plasma solutions for the lower divertor used for the simulations of impurity injection can be seen in figures 5.2, 5.3 and 5.4. As described in section
1.4.5 these simulations are base on the magnetic equilibrium reconstruction
and experimental data. The standard approach is to use measured data at
the targets and midplane. In this case this data is provided by divertor Langmuir probes (see section 3.2.4) and the MAST Thomson scattering system
(see section 3.2.4).
112
5.2 Plasma solution
Uncertainties in data location
As stated in the previous section there is significant uncertainty in the magnetic equilibrium used, which translates into an error in the radial location of
the target and midplane data used in the simulation. A sensitivity scan was
carried out to address this issue, background plasma simulations were carried
out while independently shifting the location of the midplane and target data
by 0.01 and 0.02 in normalised poloidal flux (ψn ) in each direction, equivalent
to approximately 7mm and 14mm at the outer divertor target and 3mm and
6mm at the midplane. This results in 8 further plasma solutions with either
the midplane or target data shifted. Simulations of impurity injection were
then carried out using a dwell time of 50µs and the result compared for the
5 background plasmas. The results of this scan can be in figures 5.5 and 5.6.
Figure 5.2: Simulated deuterium density and temperature for shot 29125 at
250ms
A shift of ψn = 0.01 has only a small effect on the carbon II emission. The
effect on the carbon III emission is significant for changes in the target data
113
5.2 Plasma solution
Figure 5.3: Simulated deuterium density and temperature for shot 29126 at
240ms
Figure 5.4: Simulated deuterium density and temperature for shot 29139 at
320ms
114
5.2 Plasma solution
for the L-mode cases and the midplane data in the H-mode case. For the
L-mode cases this is likely due to the change in temperature caused by the
shift, resulting in less carbon reaching the second ionisation state. In the case
of the H-mode data this reflects the large gradient in midplane temperature
and density.
A shift of ψn = 0.02 has a relatively small effect on the L-mode shot
29125, probably because the injection point is well above the targets. For
L-mode shot 29126 and H-mode shot 29139 this level of shift has a dramatic
effect on the simulation result, in particular for midplane data.
The effect on the parallel density of shifting the input data can be seen in
figure 5.7. It can be seen that the density profile changes significantly with
shifts in the input data, and helps to explain the differences seen in emission
from simulation.
Similarity between the L-mode shots
Shots 29125 and 29126 are naturally very similar, the only systematic difference being the strike point position. This is born out by a comparison
of the parallel density for the tubes just outside the strikepoint, in this case
12 and 13, which can be seen in figure 5.8. The data for tube 13 can be
taken as identical as expected, there is however a difference in the gradient
for tube 12, which is closer to the strikepoint. This is due to differences in
the midplane data, and is small enough to be unlikely to have a significant
effect on the impurity simulations.
5.2.3
Flow comparisons
The coherence imaging data allowed direct comparison of the simulated background plasma to the data. Figure 5.9 shows the measured flow compared
115
5.3 Simulated impurity injection initial conditions
against the simulated flow along one of the simulation flux tubes. It can be
seen that the measured flow profiles are largely flat in the lower divertor and
are unlike the simulated profiles which show almost zero flow along most of
the flux tube and large increase in flow towards the divertor close to the outer
target. The measured flow velocities are also significantly different from simulation. It should be noted that the lack of carbon III emission close to the
targets increases the error on this measurement and in the case of shot 29139
the measured flow close to 0ms−1 near the targets is not reliable. This casts
some doubt on the validity of the OSM background plasma simulation and
further work is required to account for this difference.
5.3
Simulated impurity injection initial conditions
There are several uncertainties associated with the injection conditions used
in the DIVIMP simulations. the principle of these are listed below.
• Initial radial position of ions relative to the outer strike point
• Initial Z position of ions
• Duration of injection
• Energy distribution of injected ions
• Number of injected ions
For each uncertainty an estimate was made from the available data. These
values were then used for the baseline simulations. Scans of these values were
then performed to identify the possible effect of the uncertainties.
116
5.3 Simulated impurity injection initial conditions
5.3.1
Initial radial position of injected impurity
The absolute radial position of the injected ions is known due to the fixed
location of the DSF at 0.985m. There is some uncertainty in this position
due to the possibility of the spark forming at a particular location on the
ring shaped gap of the injector head (see 2.4.1) instead of uniformly around
the ring. However, as the inner diameter of the outer electrode is only 2mm
any error introduced by this possibility is small. The radial position of the
injection relative to the outer strike point is harder to identify, largely due to
uncertainties in the magnetic reconstruction. Assuming the true location of
the injector then this distance is set by the simulation grid that is based on the
magnetic equilibrium. Unfortunately there is a large discrepancy between the
EFIT strike point data and that inferred from Langmuir probe measurements
(see section 3.2.3). This discrepancy can be somewhat accounted for by
moving the injection location radially in the simulation. Simulations with
injection performed at different radial locations are discussed in section 5.5.2
5.3.2
Initial Z position
Identifying the vertical or Z location of the injected ions relies on the interpretation of the filtered images (see section 4.3. This uncertainty arises
as the carbon injector launches carbon neutrals and ions vertically into the
tokamak. This can result in a vertical displacement of the carbon before
interaction with the plasma dominates their motion. This is made more difficult by the 2D projection of the 3D plume and by the mix of ions, atoms
and fine dust particles launched by the injector. Ablated ions will be confined by the toroidal magnetic field so one can be confident that the injection
location for ions is close to the centre of the DSF. The images and field line
117
5.3 Simulated impurity injection initial conditions
projections for shots 29126 and 29139 support this with the most significant
emission in the first frame after injection coming from close to the DSF location, although in shot 29126 there is significant spread in the image. Neutral
carbon particles can however travel away from the injection location until
they are ionised by the background plasma. The image from 29125 suggests
that this does occur as the emission peak appears some centimetres above the
DSF location. For the purposes of simulation the baseline injection location
for shots 29126 and 29139 was taken to be 1mm above the DSF while for
shot 29125 it was taken to be 4.5cm above the DSF.
5.3.3
Injection duration
Measurements of the discharge current and the peak in visible emission give
injection durations of approximately 40µs for the L-mode cases and 60µs for
the H-mode cases, see section 3.2.2. Although there is significant uncertainty
in these values it is reasonable to assume that the injection does in fact
take place over the duration of the imaging for purposes of comparison with
simulation.
5.3.4
Initial energy distribution
DIVIMP assigns the same energy to all injected ions, there is no possibility
of assigning an energy distribution function in a single simulation, although
this can be approximated by performing multiple simulations with different
energies and total number of injected ions and then combining the results,
this was not done here. No measurements of ion energy were made during
the development of the injector, and even if this was the case the markedly
different conditions present on MAST would cast doubt on the applicability
118
5.3 Simulated impurity injection initial conditions
of the measurements. It is therefore necessary to make an estimate of the
initial ion energy based on the available information.
The transit time of a carbon ion between the electrodes is of the order
of nanoseconds, significantly longer than the microsecond timescale of the
discharge itself. This means that individual carbon ions will gain a large
proportion of the energy available from the electric field, potentially hundreds of electron-volts. However these ions will then impact on the positive
electrode, knocking further atoms and ions from the electrodes, losing energy
to the wall and ablated products in the process. Further ionisation of the ion
is also likely to occur at these energies, further reducing the kinetic energy
of the ion. These processes are extremely complex and a detailed analysis
is beyond the scope of this thesis. However this process is very similar to
the sputtering of atoms from the first wall of fusion devices. Much research
has gone into this process and a brief discussion is available from Stangeby
[5]. This works approximates the energy distribution of physically sputtered
neutrals as
dY
EZ
=
dEZ
(EZ + EB )3
(5.7)
where Y is the sputtering yield, EZ the energy of the emitted neutral
and EB the binding energy of carbon. This distribution has a maximum at
EZ = 1/2EB , for carbon EB = 7.4eV . Although this treatment applies to
neutrals it is not unreasonable to expect carbon ions to have similar energies
in the 1eV to 10eV range.
The operation of the carbon injector can also be compared to the recent
developments in vacuum arc plasmas, on which a significant body of work
exists [165–167]. As part of this work measurements have been made of the
ion energy distribution produced by these devices. Byon 2003 [168] produced
119
5.3 Simulated impurity injection initial conditions
energy distribution functions for carbon plasmas, the result being a peaked
distribution with a high energy tail centred around 50eV - although higher
than values estimated from sputtering arguments, this is consistent with ion
energies in the 10eV range.
Although there is still large uncertainty in the initial energy of the injected
ions these arguments suggest 10eV as an appropriate initial condition and
this is used in the basic comparison with experiment.
Effect of injected energy
In order to understand the effect of ion energy on transport a scan in injected
energy was performed for the three shots of interest. Ions were injected
into the plasma with energies of 0.1eV, 1eV, 10eV and 100eV. The rate of
transport parallel to the field for the carbon II and carbon III states was
then compared for each energy. The results can be seen in figures 5.10, 5.11
and 5.12. The solid, dashed and dotted lines represent injection at 1eV,
0.1eV and 10eV while the triangles represent injection at 100eV. It can be
seen that the initial energy has a very significant impact on the impurity
transport. This is not surprising as the background plasma temperature is
approximately 10eV, once the initial energy is comparable to this value then
the pressure term in equation 1.11 becomes increasingly important.
5.3.5
Number of injected ions
The Monte Carlo method used by DIVIMP does not affect the background
plasma solution, the number of injected ions is therefore only relevant when
considering the statistical fluctuations in the solution. A higher number
of injected ions gives a result with lower statistical error at the expense of
computational resources. For the simulations described here 10000 particles
120
5.4 Parallel transport simulations for comparison with experiment
were injected, giving run times of the order of minutes.
5.4
Parallel transport simulations for comparison with experiment
In order to compare simulation with experiment DIVIMP was set up to
output the carbon II and carbon III emission along the flux tubes near to
the injection location. For the three shots 29125, 29126 and 29139, figures
5.13, 5.15 and 5.15 show the simulated carbon II and carbon III emission
along 3 flux tubes, 1 inside the outer strike point and 2 outside. 6 successive
times separated by 13.3µs are shown in each frame, the radial location of
the centre of the flux tube at the divertor target is shown above each frame.
The injection location is at the DSF location of 0.985m and the initial ion
energy is 10eV . The height of injection for shot 29125 is 4.5cm above the
target and for 29126 and 29139 it is 1mm above the target.
5.5
Comparison between experiment and simulation
Presented here are comparisons between the simulated impurity emission
along a field line corresponding to the experimentally measured emission
taken from the projection of the field lines onto the images taken by the
fast filtered cameras. An immediately obvious problem is the 3 dimensional
nature of the emission compared to the 2 dimensional images, which takes a
line of sight integrated measurement at each pixel. This problem is somewhat
alleviated by the preferential transport along the field lines. For the H-mode
121
5.5 Comparison between experiment and simulation
shot 29139 the emission can clearly be seen to follow the field line with little
cross-field transport occurring over the period of the images. This is not
the case for the 2 L-mode shots 29125 and 29126 where clear cross field
transport is observed. However strong parallel transport is still present with
the plume extending significantly along the field lines, particularly for shot
29126. The diffuse nature of the emission in shot 29125 is likely due to the
injection location, which appears to have occurred radially inside the outer
strike point. The diffuse nature may then be partly due to neutral particles
being injected upwards in an expanding cloud and ionising once they reach
the hotter denser region close to the separatrix, in a manner more akin to
gas injection.
Figures 5.16, 5.17 and 5.18 show the experimentally measured carbon II
emission plotted against the simulated carbon II emission for the flux tube
with the highest emission in each case for the 2 L-mode and 1 H-mode shot.
The initial conditions are the same as the plots presented in section 5.4 and
an arbitrary normalisation factor has been applied to the simulated emission
of 16 in the case of comparison with sector 1 data and 128 in the case of
comparison with sector 11 data. No comparison is made with carbon III
data due to the lack of observed emission.
5.5.1
Lack of observed CIII emission
As has been noted in section 4.3.2 very little or no extended emission was seen
when using carbon III filters. Looking at the ratio of carbon II to carbon III
emission from simulation one can see that the carbon III emission is at least
a factor 10 below the carbon II emission. The maximum observed carbon
III emission is approximately 5W sr−1 m−2 from sector 11 shot 29142, while
the maximum observed carbon II emission is approximately 10W sr−1 m−2.
122
5.5 Comparison between experiment and simulation
However this is found at the injection location and the large peak in emission
seen in experiment is not seen in simulation, suggesting that this level of
emission is at least partly due to the arc discharge itself. Looking at the
carbon II images (figure 4.8) one can see that the intensity in the plume away
from the injection location is typically 0.5W sr−1 m−2, assuming a ratio of
10:1 between the carbon II and carbon III emission the carbon II emission
would be of the order 5 × 10−2 W sr−1 m−2, only just above the noise level of
3 × 10−2 W sr−1 m−2. The most likely reason for a lack of observed emission
is therefore a lack of sensitivity of the filtered cameras.
5.5.2
Effect of radial location on emission
In order to account for the errors in strike point location calculated by EFIT
runs were performed for shots 29125 and 29139 with the injection location
moved by 1cm and 2cm. This changes the tube within which the highest
emission occurs and so changes the tube used for comparison. For shot 29125
the adjustment was made inwards towards the high field side, increasing the
distance of the injection inside the outer strike point, this can be seen in
figure 5.19. For shot 29139 the calculated strike point was clearly outside
the true location, 1cm and 2cm adjustments were therefore made towards
the low field side and can be seen in figure 5.20. Only plots for sector 1 are
shown.
5.5.3
Relative contribution of the transport mechanisms
As described in sections 1.2.3 and 5.1.3 there are several mechanisms responsible for the transport of impurities, either corresponding to a term in
123
5.6 Role of drift terms in simulation results
equation 1.11 or added to account for unknown physics as in the case of the
cross-field diffusion coefficient. To better understand the importance of each
mechanism in these simulations a series of simulations were carried out with
the relevant term suppressed. The simulations were run with a dwell time of
50µs and the results can be seen in figure 5.21.
In each case the left panel shows the suppression of forces due to the
temperature gradient, friction and electric field, it can be seen that for 29125
these do not have a significant effect on the result. For 29126 the temperature gradient has little effect although the forces due to the electric field and
friction do have a small but noticeable effect, this is likely due to the high
flow and electric fields close to the target. For the H-mode 29139 only the
frictional force has a significant effect. The middle panel shows simulations
run without collisions and with the cross-field diffusion set to 0. Switching
off collisions, which has the effect of suppressing diffusion, has the effect of
increasing the parallel transport. Switching off the cross-field diffusion increases the emission for this tube, this is expected as more particles remain
in the tube into which the injection occurred. The right panel shows impurities injected with 0 energy, this appears to be the most significant factor in
determining transport, and also explains why turning off collisions increases
the parallel transport by such an extent.
5.6
Role of drift terms in simulation results
It has previously been stated that neither DIVIMP or OSM simulations
include drift terms arising from electric field and magnetic field gradients.
Recent research has focused on the impact of particle drifts on impurity
transport[133] and divertor plasma conditions[96, 112, 169] and has shown
124
5.6 Role of drift terms in simulation results
these terms to be important in accurately representing carbon deposition
and target power loads. How important these terms are with regards to the
parallel impurity transport, which governs the influx of impurities sputtered
from the target into the bulk plasma is less clear.
5.6.1
Effect of drift terms on background plasma solution
Particle drifts can have a variety of effects on the background plasma conditions, which will then affect the transport of impurities.
It has been
shown[112, 170] that E × B and diamagnetic drifts cause a broadening of
the outer target radial profile and a reduction in peak density and power
reaching the target. However this effect is implicitly included in the OSM
modelling approach through the anomalous source terms and the prescription of target profiles from experimental data. Effects of drifts on the plasma
profiles along B are however not included using this method. In particular
the parallel flow appears to be significantly affected by drifts [112, 171], with
simulations on JT-60[169] showing mid-plane flow velocities increasing from
2.5kms−1 to 8.3kms−1 when drift velocities are included. This is strongly
supported by data from the coherence imaging diagnostic used in these experiments (section 5.2.3), which shows a significantly higher flow velocity than
seen from simulation along most of the flux tube. The effect of increased
flow is to increase the force on the impurity ions due to friction and for the
2 cases with injection close to the target, L-mode shot 29126 and H-mode
shot 29139, this term is seen to be significant (section 5.5.3). The simulated
flow close to the targets is actually larger than the measured flow, so that the
significance of the friction term may be doubted, while further away from the
targets as in shot 29125, where the frictional force appears less significant,
125
5.6 Role of drift terms in simulation results
the opposite is true. It can therefore be inferred that the simulated flow has
a significant impact on the validity of the impurity transport simulations.
5.6.2
Direct impact of drift terms on plume evolution
The effect of E × B drifts on injected impurity plumes has previously been
observed by imaging of the plume distortion[51] and also by measuring the
location of deposited carbon-13[133] from post-mortem analysis of divertor
tiles. For standard magnetic field direction (∇B drift towards the lower divertor) radial electric fields in the divertor SOL caused by radial temperature
gradients result in a poloidal drift towards the outer target, while electric
fields parallel to the magnetic field caused by parallel temperature gradients
cause an inward radial drift towards the private flux region. Electric fields
in the magnetic presheath to the sheath can also cause radial drifts, however
identification of this effect in the plumes studied here is not possible as it
occurs within approximately 1mm of the targets and can only be inferred
using post-mortem analysis techniques and detailed modelling[133].
The extremely diffuse nature of the plume in shot 29125 means that any
distortion is obscured, however for shots 29126 and 29139 the plume closely
follows the field lines towards the X-point. The orientation of the sector
1 camera means that the radial and poloidal drifts work in approximately
opposite directions in the image plane and partially cancel out the observed
distortion. The sector 11 camera suffers less from this problem as the radial
drifts are largely normal to the image plane, while the poloidal drifts are
largely vertical, the approximate directions are seen in figure 5.22. Comparing figure 5.22 a and b one can see an apparent distortion in the plume in
the poloidal direction towards the targets that is more pronounced in the
sector 11 image. This could be interpreted as the effect of a poloidal drift,
126
5.6 Role of drift terms in simulation results
however errors in the magnetic equilibrium reconstruction and magnetic field
projection due to the camera registration could cause a similar effect.
127
5.6 Role of drift terms in simulation results
CII emission
0.035
0.025
0.020
0.015
0.010
0.005
0.000
0.0
standard
midplane+
midplanetarget+
target-
0.0030
Emission (arb.)
Emission (arb.)
0.030
CIII emission
0.0035
standard
midplane+
midplanetarget+
target-
0.0025
0.0020
0.0015
0.0010
0.0005
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(a) 29125
CII emission
0.045
0.030
0.025
0.020
0.015
0.010
0.0020
0.0015
0.0010
0.0005
0.005
0.000
0.0
standard
midplane+
midplanetarget+
target_
0.0025
Emission (arb.)
Emission (arb.)
0.035
CIII emission
0.0030
standard
midplane+
midplanetarget+
target_
0.040
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(b) 29126
CII emission
standard
midplane+
midplanetarget+
target-
Emission (arb.)
0.0015
0.0010
standard
midplane+
midplanetarget+
target-
0.00015
0.0005
0.0000
0.0
CIII emission
0.00020
Emission (arb.)
0.0020
0.00010
0.00005
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.00000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(c) 29139
Figure 5.5: Sensitivity scan using background plasma solutions with the
target or midplane data shifted by ψn ± 0.01. Each plot shows simulated
carbon II and carbon III emission parallel to the magnetic field from the
injection location. s is the parallel distance along the flux tube.
128
5.6 Role of drift terms in simulation results
CII emission
0.035
0.025
0.020
0.015
0.010
0.005
0.000
0.0
standard
midplane+
midplanetarget+
target-
0.0030
Emission (arb.)
Emission (arb.)
0.030
CIII emission
0.0035
standard
midplane+
midplanetarget+
target-
0.0025
0.0020
0.0015
0.0010
0.0005
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(a) 29125
CII emission
0.045
0.030
0.025
0.020
0.015
0.010
0.0020
0.0015
0.0010
0.0005
0.005
0.000
0.0
standard
midplane+
midplanetarget+
target_
0.0025
Emission (arb.)
Emission (arb.)
0.035
CIII emission
0.0030
standard
midplane+
midplanetarget+
target_
0.040
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(b) 29126
CII emission
standard
midplane+
midplanetarget+
target-
Emission (arb.)
0.0025
0.0020
0.0015
0.0010
standard
midplane+
midplanetarget+
target-
0.00020
0.00015
0.00010
0.00005
0.0005
0.0000
0.0
CIII emission
0.00025
Emission (arb.)
0.0030
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.00000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(c) 29139
Figure 5.6: Sensitivity scan using background plasma solutions with the
target or midplane data shifted by ψn ± 0.02. Each plot shows simulated
carbon II and carbon III emission parallel to the magnetic field from the
injection location. s is the parallel distance along the flux tube.
129
5.6 Role of drift terms in simulation results
3
Density (m− )
3.0
2.5
4.0 1e18
3.5
3.0
3
3.5
29125 Density
standard
mid+
midtarget+
target-
Density (m− )
4.0 1e18
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.00.0
2.5
29125 Density
standard
mid++
mid-target++
target--
0.5
0.5
1.0
s (m)
1.5
0.00.0
2.0
0.5
1.0
s (m)
1.5
2.0
1.5
2.0
1.5
2.0
(a) 29125
3
Density (m− )
3.0
2.5
4.0 1e18
3.5
3.0
3
3.5
29126 Density
standard
mid+
midtarget+
target-
Density (m− )
4.0 1e18
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.00.0
2.5
29126 Density
standard
mid++
mid-target++
target--
0.5
0.5
1.0
s (m)
1.5
0.00.0
2.0
0.5
1.0
s (m)
(b) 29126
3
Density (m− )
2.5
4.0 1e18
3.5
3.0
3
3.5
3.0
29139 Density
standard
mid+
midtarget+
target-
Density (m− )
4.0 1e18
2.0
2.5
29139 Density
standard
mid++
mid-target++
target--
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.00.0
0.00.0
0.5
1.0
s (m)
1.5
2.0
0.5
1.0
s (m)
(c) 29139
Figure 5.7: Density along the magnetic field for the simulation tube where
the injection takes place.
130
5.6 Role of drift terms in simulation results
4.0 1e18 29125 vs 29126 Density
3.5
3
Density (m− )
3.0
29125-12
29125-13
21926-12
21926-13
2.5
2.0
1.5
1.0
0.5
0.00.0
0.5
1.0
s (m)
1.5
2.0
Figure 5.8: Density along the magnetic field for simulation tubes just outside
the strike points for shots 29125 and 29126. The data for tube 13 can be
taken as identical as expected, there is however a difference in the gradient
for tube 12, which is closer to the strikepoint. This is due to differences in
the midplane data, and is small enough to be unlikely to have a significant
effect on the impurity simulations.
131
5.6 Role of drift terms in simulation results
30000
−1.0
10000
0
−1.5
−4
−12
−16
−10000
−2.0
−20000
−30000
0
−8
Z (m)
Flow velocity (ms−1 )
4
Simulated flow
Measured flow
20000
−20
−24
−28
8
9
10
11
12
s (m)
13
14
15
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
R (m)
(a) 29125
30000
Simulated flow
Measured flow
0
−1.0
10000
0
−1.5
−2.0
−20000
−24
−32
−10000
−30000
−8
−16
Z (m)
Flow velocity (ms−1 )
20000
−40
−48
−56
9
10
11 12 13 14
s (m)
15 16
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
R (m)
(b) 29126
30000
Simulated flow
Measured flow
8
−1.0
0
−1.5
−16
−24
−32
−10000
−2.0
−20000
−30000
0
−8
10000
Z (m)
Flow velocity (ms−1 )
20000
−40
−48
7
8
9
10
s (m)
11
12
13
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
R (m)
−56
(c) 29139
Figure 5.9: Comparison of measured and simulated parallel flow using the
coherence imaging diagnostic and carbon III emission lines, see section 1.3.1.
132
5.6 Role of drift terms in simulation results
0.0015
0.0010
0.003
0.002
0.0005
0.0000
0.0
0.004
0.1
0.2
0.3
s (m)
0.4
0.5
0.006
0.004
0.1
0.2
0.3
s (m)
0.4
0.000
0.6
0.0
0.5
CII 40µs
0.012
0.1eV
1.0eV
10eV
100eV
0.010
0.008
0.006
0.004
0.002
0.001
0.000
0.6
0.0
0.1eV
1.0eV
10eV
100eV
0.008
Emission
0.005
CII 30µs
0.010
0.1eV
1.0eV
10eV
100eV
0.006
Emission
Emission
0.0020
CII 20µs
0.007
0.1eV
1.0eV
10eV
100eV
0.0025
Emission
CII 10µs
0.0030
0.002
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(a) CII emission
0.00010
0.00008
0.00006
0.0005
0.0004
0.0003
0.1
0.2
0.3
s (m)
0.4
0.5
0.0000
0.6
0.0
0.1eV
1.0eV
10eV
100eV
0.0008
0.0006
0.1
0.2
0.3
s (m)
0.4
0.5
0.0000
0.6
0.0
CIII 40µs
0.0016
0.1eV
1.0eV
10eV
100eV
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0001
0.00002
CIII 30µs
0.0012
0.0010
0.0004
0.0002
0.00004
0.00000
0.0
0.1eV
1.0eV
10eV
100eV
Emission
Emission
0.00012
CIII 20µs
0.0007
0.0006
Emission
0.1eV
1.0eV
10eV
100eV
Emission
CIII 10µs
0.00016
0.00014
0.0002
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(b) CIII emission
Figure 5.10: Comparison of transport parallel to the magnetic field for CII
and CIII ions injected at 0.1eV, 1eV , 10eV and 100eV at 10µs, 20µs, 30µs
and 40µs after injection for shot 29125. s is the distance along the magnetic
field from the lower target.
133
5.6 Role of drift terms in simulation results
0.15
0.10
0.10
0.10
0.05
0.05
0.05
0.05
0.00
0.0
0.00
0.0
0.00
0.0
0.2
0.3
s (m)
0.4
0.5
0.6
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.1
0.2
0.3
s (m)
0.4
0.5
0.1eV
1.0eV
10eV
100eV
0.15
0.00
0.0
0.1
CII 40µs
0.20
0.1eV
1.0eV
10eV
100eV
Emission
0.10
CII 30µs
0.20
0.1eV
1.0eV
10eV
100eV
0.15
Emission
Emission
0.15
CII 20µs
0.20
0.1eV
1.0eV
10eV
100eV
Emission
CII 10µs
0.20
0.6
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(a) CII emission
0.0008
0.0006
0.0010
0.0008
0.0006
0.0004
0.0004
0.0002
0.0002
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.1eV
1.0eV
10eV
100eV
0.0012
0.6
0.0000
0.0
CIII 30µs
0.0016
0.1eV
1.0eV
10eV
100eV
0.0014
0.0012
0.0010
0.0008
0.0006
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.0015
0.0010
0.6
0.0000
0.0
0.0005
0.0002
0.2
0.1eV
1.0eV
10eV
100eV
0.0020
0.0004
0.1
CIII 40µs
0.0025
Emission
Emission
0.0010
CIII 20µs
0.0014
Emission
0.1eV
1.0eV
10eV
100eV
0.0012
Emission
CIII 10µs
0.0014
0.1
0.2
0.3
s (m)
0.4
0.5
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(b) CIII emission
Figure 5.11: Comparison of transport parallel to the magnetic field for CII
and CIII ions injected at 0.1eV, 1eV , 10eV and 100eV at 10µs, 20µs, 30µs
and 40µs after injection for shot 29126. s is the distance along the magnetic
field from the lower target.
134
5.6 Role of drift terms in simulation results
0.00020
0.00015
0.00010
0.0003
0.0002
0.1
0.2
0.3
s (m)
0.4
0.5
0.0000
0.6
0.0
CII 30µs
0.0010
0.1eV
1.0eV
10eV
100eV
0.0008
0.0001
0.00005
0.00000
0.0
0.1eV
1.0eV
10eV
100eV
0.0006
0.0004
0.1
0.2
0.3
s (m)
0.4
0.5
0.1eV
1.0eV
10eV
100eV
0.0008
0.0006
0.0004
0.0002
0.0000
0.6
0.0
CII 40µs
0.0012
0.0010
Emission
Emission
0.00025
CII 20µs
0.0005
0.0004
Emission
0.1eV
1.0eV
10eV
100eV
Emission
CII 10µs
0.00035
0.00030
0.0002
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(a) CII emission
0.000004
0.000008
0.000006
0.1
0.2
0.3
s (m)
0.4
0.5
0.00003
0.000002
0.00001
0.000000
0.6
0.0
0.00000
0.6
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
CIII 40µs
0.00009
0.1eV 0.00008
1.0eV
0.00007
10eV
100eV 0.00006
0.00002
0.000004
0.000002
CIII 30µs
0.00006
0.1eV
1.0eV 0.00005
10eV
100eV 0.00004
Emission
0.000006
Emission
Emission
0.000008
0.000000
0.0
CIII 20µs
0.000014
0.1eV
1.0eV 0.000012
10eV 0.000010
100eV
Emission
CIII 10µs
0.000010
0.1eV
1.0eV
10eV
100eV
0.00005
0.00004
0.00003
0.00002
0.00001
0.1
0.2
0.3
s (m)
0.4
0.5
0.00000
0.6
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(b) CIII emission
Figure 5.12: Comparison of transport parallel to the magnetic field for CII
and CIII ions injected at 0.1eV, 1eV , 10eV and 100eV at 10µs, 20µs, 30µs
and 40µs after injection for shot 29139. s is the distance along the magnetic
field from the lower target.
135
5.6 Role of drift terms in simulation results
0.0008
0.0006
13µs
27µs
40µs
53µs
67µs
0.006
0.005
Emission
Emission
0.0010
CII Tube 12 0.995m
0.007
13µs
27µs
40µs
53µs
67µs
0.0012
0.004
0.003
0.020
0.015
0.010
0.002
0.0002
0.001
0.005
0.0000
0.0
0.000
0.0
0.000
0.0
0.2
0.3
s (m)
0.4
0.5
0.6
13µs
27µs
40µs
53µs
67µs
0.025
0.0004
0.1
CII Tube 13 1.016m
0.030
Emission
CII Tube 59 0.986m
0.0014
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(a) CII emission
Emission
0.00025
0.00020
0.00015
13µs
27µs
40µs
53µs
67µs
0.0012
0.00010
0.0010
0.0008
0.0006
0.2
0.3
s (m)
0.4
0.5
0.6
13µs
27µs
40µs
53µs
67µs
0.0035
0.0030
0.0025
0.0020
0.0015
0.0010
0.0002
0.1
CIII Tube 13 1.016m
0.0040
0.0004
0.00005
0.00000
0.0
CIII Tube 12 0.995m
0.0016
0.0014
Emission
13µs
27µs
40µs
53µs
67µs
Emission
CIII Tube 59 0.986m
0.00035
0.00030
0.0005
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(b) CIII emission
Figure 5.13: Comparison of transport parallel to the magnetic field for CII
(a) and CIII (b) ions injected into shot 29125. Each frame shows emission
along a different flux tube starting at radial locations 0.986m, 0.995m and
1.016m. s is the distance along the magnetic field from the lower target.
136
5.6 Role of drift terms in simulation results
0.0015
0.035
0.030
0.025
0.020
0.020
0.2
0.3
s (m)
0.4
0.5
0.6
0.015
0.010
0.005
0.005
0.1
13µs
27µs
40µs
53µs
67µs
0.025
0.010
0.0005
CII Tube 13 0.990m
0.030
0.015
0.0010
0.0000
0.0
13µs
27µs
40µs
53µs
67µs
0.040
Emission
Emission
0.0025
0.0020
CII Tube 12 0.982m
0.045
13µs
27µs
40µs
53µs
67µs
Emission
CII Tube 59 0.975m
0.0035
0.0030
0.000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(a) CII emission
Emission
0.00015
0.00010
13µs
27µs
40µs
53µs
67µs
0.0020
0.00005
0.00000
0.0
CIII Tube 12 0.982m
0.0025
Emission
13µs
27µs
40µs
53µs
67µs
0.0015
0.0010
0.2
0.3
s (m)
0.4
0.5
0.6
13µs
27µs
40µs
53µs
67µs
0.0015
0.0010
0.0005
0.0005
0.1
CIII Tube 13 0.990m
0.0020
Emission
CIII Tube 59 0.975m
0.00020
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(b) CIII emission
Figure 5.14: Comparison of transport parallel to the magnetic field for CII
(a) and CIII (b) ions injected into shot 29126. Each frame shows emission
along a different flux tube starting at radial locations 0.975m, 0.982m and
0.990m. s is the distance along the magnetic field from the lower target.
137
5.6 Role of drift terms in simulation results
Emission
0.030
0.025
0.020
13µs
27µs
40µs
53µs
67µs
0.016
0.014
0.012
Emission
0.035
CII Tube 7 0.993m
0.018
13µs
27µs
40µs
53µs
67µs
0.010
0.008
0.0012
0.0010
0.0008
0.006
0.0006
0.010
0.004
0.0004
0.005
0.002
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.000
0.0
13µs
27µs
40µs
53µs
67µs
0.0014
0.015
0.000
0.0
CII Tube 8 1.00m
0.0018
0.0016
Emission
CII Tube 45 0.983m
0.045
0.040
0.0002
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.0000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(a) CII emission
0.0006
Emission
0.0005
0.0004
0.0003
13µs
27µs
40µs
53µs
67µs
0.0005
0.0004
0.0003
0.0002
0.0002
0.1
0.2
0.3
s (m)
0.4
0.5
0.0000
0.6
0.0
CIII Tube 8 1.00m
0.00012
13µs
27µs
40µs
53µs
67µs
0.00010
0.00008
0.00006
0.00004
0.0001
0.0001
0.0000
0.0
CIII Tube 7 0.993m
0.0006
Emission
13µs
27µs
40µs
53µs
67µs
Emission
CIII Tube 45 0.983m
0.0007
0.00002
0.1
0.2
0.3
s (m)
0.4
0.5
0.00000
0.6
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(b) CIII emission
Figure 5.15: Comparison of transport parallel to the magnetic field for CII
(a) and CIII (b) ions injected into shot 29139. Each frame shows emission
along a different flux tube starting at radial locations 0.983m, 0.993m and
1.00m. s is the distance along the magnetic field from the lower target.
138
5.6 Role of drift terms in simulation results
CII 13µs
0.25
Emission (arb.)
0.20
0.15
0.10
0.05
CII 40µs
Simulation
Experiment
0.20
0.25
Emission (arb.)
0.25
Emission (arb.)
CII 27µs
Simulation
Experiment
0.15
0.10
0.05
Simulation
Experiment
0.20
0.15
0.10
0.05
0.00
0.00
0.00
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
s (m)
s (m)
s (m)
CII 53µs
0.25
0.20
0.15
0.10
0.05
Simulation
Experiment
0.25
Emission (arb.)
Emission (arb.)
CII 67µs
Simulation
Experiment
0.20
0.15
0.10
0.05
0.00
0.00
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
s (m)
s (m)
(a) Sector 1 emission
CII 10µs
Emission (arb.)
0.6
0.4
CII 20µs
1.0
Simulation
Experiment
0.8
0.6
0.4
CII 30µs
Simulation
Experiment
0.8
0.6
0.4
0.2
0.2
0.2
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
s (m)
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
s (m)
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
s (m)
1.0
1.0
1.0
Simulation
Experiment
0.6
0.4
0.8
CII 50µs
Simulation
Experiment
0.6
0.4
0.8
Emission (arb.)
0.8
CII 40µs
Emission (arb.)
Emission (arb.)
0.8
Emission (arb.)
1.0
Simulation
Experiment
Emission (arb.)
1.0
CII 60µs
Simulation
Experiment
0.6
0.4
0.2
0.2
0.2
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
s (m)
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
s (m)
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
s (m)
(b) Sector 11 emission
Figure 5.16: Comparison with experiment of transport parallel to the magnetic field for CII ions for L-mode shot 29125. s is the distance along the
magnetic field from the lower target.139
5.6 Role of drift terms in simulation results
CII 13µs
CII 27µs
Simulation
Experiment
1.4
1.4
0.6
1.2
1.0
Emission (arb.)
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.2
0.1
0.2
0.3
s (m)
0.4
0.0
0.0
0.5
0.1
0.2
CII 53µs
0.3
s (m)
0.4
0.0
0.0
0.5
0.1
0.2
CII 67µs
Simulation
Experiment
1.4
1.2
1.2
1.0
1.0
0.8
0.6
0.4
0.3
s (m)
0.4
0.5
Simulation
Experiment
1.4
Emission (arb.)
Emission (arb.)
1.0
0.8
0.4
0.0
0.0
Simulation
Experiment
1.4
1.2
Emission (arb.)
Emission (arb.)
1.2
CII 40µs
Simulation
Experiment
0.8
0.6
0.4
0.2
0.2
0.0
0.0
0.0
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.1
0.2
0.3
s (m)
0.4
0.5
(a) Sector 1 emission
CII 10µs
5
Emission (arb.)
4
3
2
1
0
0.0
4
3
2
0.1
0.2
0.3
s (m)
0.4
0
0.0
0.5
0.1
0.2
0.3
s (m)
0.4
2
1
0.1
0.4
0.5
Simulation
Experiment
4
3
2
0
0.0
0.2
0.3
s (m)
0.4
0.5
CII 60µs
1
0.3
s (m)
2
0
0.0
0.5
Simulation
Experiment
5
Emission (arb.)
3
0.2
3
1
5
Emission (arb.)
Emission (arb.)
4
0.1
4
CII 50µs
Simulation
Experiment
5
Simulation
Experiment
5
1
CII 40µs
0
0.0
CII 30µs
Simulation
Experiment
Emission (arb.)
5
Emission (arb.)
CII 20µs
Simulation
Experiment
4
3
2
1
0.1
0.2
0.3
s (m)
0.4
0.5
0
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
(b) Sector 11 emission
Figure 5.17: Comparison with experiment of transport parallel to the magnetic field for CII ions for L-mode shot 29126. s is the distance along the
140
magnetic field from the lower target.
5.6 Role of drift terms in simulation results
CII 13µs
1.0
0.5
0.0
0.0
1.5
1.0
0.5
0.1
0.2
0.3
s (m)
0.4
0.0
0.0
0.5
Simulation
Experiment
0.1
0.2
0.3
s (m)
0.4
0.0
0.0
0.5
0.1
0.2
1.0
0.5
0.3
s (m)
0.4
0.5
Simulation
Experiment
2.0
Emission (arb.)
Emission (arb.)
1.0
CII 67µs
1.5
0.0
0.0
1.5
0.5
CII 53µs
2.0
Simulation
Experiment
2.0
Emission (arb.)
1.5
CII 40µs
Simulation
Experiment
2.0
Emission (arb.)
2.0
Emission (arb.)
CII 27µs
Simulation
Experiment
1.5
1.0
0.5
0.1
0.2
0.3
s (m)
0.4
0.0
0.0
0.5
0.1
0.2
0.3
s (m)
0.4
0.5
(a) Sector 1 emission
CII 10µs
4
2
0
0.0
6
4
2
0.1
0.2
0.3
s (m)
0.4
0
0.0
0.5
Simulation
Experiment
0.1
0.2
0.3
s (m)
0.4
2
0.3
s (m)
0.1
0.4
0.5
0.3
s (m)
0.4
0.5
4
Simulation
Experiment
8
Emission (arb.)
6
0
0.0
0.2
CII 60µs
2
0.2
0
0.0
0.5
Simulation
Experiment
8
Emission (arb.)
Emission (arb.)
4
0.1
4
CII 50µs
6
0
0.0
6
2
CII 40µs
8
Simulation
Experiment
8
Emission (arb.)
6
CII 30µs
Simulation
Experiment
8
Emission (arb.)
8
Emission (arb.)
CII 20µs
Simulation
Experiment
6
4
2
0.1
0.2
0.3
s (m)
0.4
0.5
0
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
(b) Sector 11 emission
Figure 5.18: Comparison with experiment of transport parallel to the magnetic field for CII ions for H-mode shot 29139. s is the distance along the
141
magnetic field from the lower target.
5.6 Role of drift terms in simulation results
0.25
0.25
0.20
Emission
Emission
0.20
CII 27µs
Simulation
Experiment
0.15
0.10
0.05
CII 40µs
Simulation
Experiment
CII 53µs
0.25
0.20
0.15
0.10
0.05
0.20
Emission
CII 13µs
Simulation
Experiment
Emission
0.25
0.15
0.10
0.05
0.15
0.10
0.05
0.00
0.00
0.00
0.00
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
s (m)
s (m)
s (m)
s (m)
(a) 1cm shift
0.25
0.15
0.10
0.05
0.25
0.20
Emission
Emission
0.20
CII 27µs
Simulation
Experiment
CII 40µs
Simulation
Experiment
CII 53µs
0.25
0.20
0.15
0.10
0.05
0.15
0.10
0.05
0.20
Emission
CII 13µs
Simulation
Experiment
Emission
0.25
0.15
0.10
0.05
0.00
0.00
0.00
0.00
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
s (m)
s (m)
s (m)
s (m)
(b) 2cm shift
Figure 5.19: Comparison with experiment of transport parallel to the magnetic field for CII ions for L-mode shot 29125. s is the distance along the
magnetic field from the lower target.
142
5.6 Role of drift terms in simulation results
6
4
2
0
0.0
6
4
2
0.1
0.2
0.3
s (m)
0.4
0
0.0
0.5
CII 40µs
Simulation
Experiment
8
Emission (arb.)
8
Emission (arb.)
Emission (arb.)
8
CII 27µs
Simulation
Experiment
6
4
2
0.1
0.2
0.3
s (m)
0.4
0
0.0
0.5
CII 53µs
Simulation
Experiment
8
Emission (arb.)
CII 13µs
Simulation
Experiment
6
4
2
0.1
0.2
0.3
s (m)
0.4
0
0.0
0.5
0.1
0.2
0.3
s (m)
0.4
0.5
(a) 1cm shift
4
2
6
4
2
0.1
0.2
0.3
s (m)
0.4
0.5
0
0.0
CII 40µs
Simulation
Experiment
8
Emission (arb.)
6
0
0.0
8
Emission (arb.)
Emission (arb.)
8
CII 27µs
Simulation
Experiment
6
4
2
0.1
0.2
0.3
s (m)
0.4
0.5
0
0.0
CII 53µs
Simulation
Experiment
8
Emission (arb.)
CII 13µs
Simulation
Experiment
6
4
2
0.1
0.2
0.3
s (m)
0.4
0.5
0
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
(b) 2cm shift
Figure 5.20: Comparison with experiment of transport parallel to the magnetic field for CII ions for H-mode shot 29139 with (a) 1cm and and (b) 2cm
shift applied to the injection location. s is the distance along the magnetic
field from the lower target.
143
5.6 Role of drift terms in simulation results
Emission (arb.)
0.025
0.020
0.015
0.010
0.030
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.06
0.025
0.015
0.05
0.04
0.03
0.010
0.02
0.005
0.01
0.1
0.2
0.3
s (m)
0.4
0.5
standard
0energy
0.07
0.020
0.000
0.0
CII emission
0.08
standard
collisions
x-field
0.035
0.005
0.000
0.0
CII emission
0.040
Emission (arb.)
standard
friction
gradT
efield
Emission (arb.)
CII emission
0.030
0.00
0.0
0.6
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(a) 29125
0.030
0.025
0.07
0.020
0.015
0.06
0.05
0.03
0.02
0.005
0.01
0.000
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.00
0.0
0.6
standard
0energy
0.15
0.04
0.010
CII emission
0.20
standard
collisions
x-field
0.08
Emission (arb.)
Emission (arb.)
0.035
CII emission
0.09
standard
friction
gradT
efield
Emission (arb.)
CII emission
0.045
0.040
0.10
0.05
0.1
0.2
0.3
s (m)
0.4
0.5
0.00
0.0
0.6
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(b) 29126
0.030
0.025
0.020
0.015
0.010
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.14
0.04
0.03
0.02
0.00
0.0
standard
0energy
0.16
0.12
0.10
0.08
0.06
0.04
0.01
0.005
0.000
0.0
0.05
CII emission
0.18
standard
collisions
x-field
0.06
Emission (arb.)
Emission (arb.)
0.035
CII emission
0.07
standard
friction
gradT
efield
Emission (arb.)
CII emission
0.045
0.040
0.02
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
0.00
0.0
0.1
0.2
0.3
s (m)
0.4
0.5
0.6
(c) 29139
Figure 5.21: Simulations with terms affecting impurity transport suppressed
for shots 29125, 29126 ad 29139. The legend indicates the force term that has
been suppressed. In each case the left panel shows the suppression of forces
due to the temperature gradient, friction and electric field, these do not have
a significant effect on the result. The middle panel shows simulations run
without collisions and with the cross-field diffusion set to 0m2 s−1 . The right
panel shows impurities injected with energy of 0eV , this appears to be the
most significant factor in determining transport. s is the distance along the
magnetic field from the lower target.
144
5.6 Role of drift terms in simulation results
(a) Sector 1
(b) Sector 11
Figure 5.22: Approximate direction of the radial and poloidal drifts in the
image plane for for sectors 1(a) and 11(b) for H-mode shot 29139 40µs after
injection. The plume appears to drift poloidally away from the magnetic field
with the effect being more pronounced in the sector 11 image. Care must be
taken in the interpretation of this due to errors in the magnetic equilibrium
and magnetic field projection.
145
CHAPTER
6
Conclusions and further work
6.1
6.1.1
Conclusions
Injection system
It has been demonstrated that the carbon injector has successfully injected
carbon atoms and ions into the MAST plasma. Diagnostic measurements
suggest that the injection does not significantly perturb the plasma and yet
is visible to cameras operating at frame rates up to 100kHz. The capacitor discharge did not affect other systems present on the machine, including
diagnostic and control systems. The simplicity of the design allows the equipment to be installed within a day, although testing of the associated systems
is also required. The light weight of the injector head and limited number of
wired connections means that this device is suitable for installation in various locations on the plasma vessel including the possibility of mounting on
146
6.1 Conclusions
reciprocating probes to allow injection into the SOL mid-plane. The financial
cost of the system is also low when compared with other injection systems
such as laser blow off.
The initialisation of the injection can be specified to within 1µs although
there is a degree of variability of the quantity of injected carbon over the
following 50µs to 100µs. There is also significant uncertainty in the number
of atoms and ions injected during the discharge. The ability to alter the
discharge voltage allows injection into different plasma conditions while still
keeping perturbation low. The final version of the system was shown to
be extremely reliable and discharged with a success rate of 100% during the
final set of experiments. The uncertainty in the energy of the injected carbon
caused significant difficulties in comparison with simulation and would need
to be addressed on future systems. The small quantity of carbon injected
keeps the perturbation of the background plasma low so that modelling need
not address the cooling associated with gas injection systems[172].
6.1.2
Modelling
The OSM approach is well suited for producing background plasma solutions for DIVIMP simulations. The use of experimental data to constrain
the solution gives confidence in its accuracy close to the targets and avoids
some of the the problems with target profiles associated with full 2D plasma
codes[112, 170]. Conversely, the limited experimental constraints used in this
study limit the validity of the solution away from the targets, this is highlighted by the disagreement between the simulated flow and that measured
by the coherence imaging diagnostic for all shots studied. Using this data
as a constraint is a natural next step in improving the background plasma
solution. The simulation of flow is an issue for full 2D codes [169, 171] as
147
6.1 Conclusions
well as OSM and highlights the value of new diagnostic techniques such as
this. The lack of drift terms in OSM is likely to play a role in the incorrect
simulation of parallel flow, although development of the code is required to
confirm this.
The errors introduced by the EFIT magnetic equilibrium reconstruction
are significant and this work highlights the importance of accurate equilibrium reconstruction as conditions in the edge plasma varying significantly
with location, as shown by the different behaviour of the carbon plume between shots 29125 and 29126, where the difference between the injection
locations relative to the outer strike point is approximately 1cm. This effect
is likely to be more pronounced in H-mode shots, which typically have a much
reduced scrape off layer width, however only one H-mode shot was imaged
while using carbon II filters. Despite this, sensitivity scans show that the
solution is robust to errors up to approximately 1cm, however beyond this
the solutions are altered significantly. The solution can be further improved
using other experimental constraints such as spectroscopic imaging of Dα
and Dγ emission[162].
The DIVIMP simulations of carbon transport based on the OSM plasma
solutions show reasonable qualitative agreement with experimental data, in
particular showing the diffuse nature of the parallel transport in L-mode
shot 29125 and the low level of parallel transport seen in the H-mode shot
29139. The results are not sensitive to small changes in the background
plasma resulting from shifting the target and target data, although shifts of
approximately 1.5cm do have a significant impact on the simulated carbon
distribution. The effect of plasma flow on carbon transport through friction
is small but significant, increasing the importance of accurately modelling
flow in the background plasma.
148
6.1 Conclusions
The simulation scan in the energy of injected ions and the study of the
principle mechanisms affecting the simulated plume evolution show that energy of the injected carbon is likely to have a significant impact on the impurity transport, so that although the injection does not appear to significantly
perturb the plasma the dynamics of the injected carbon are dominated by
the injection energy and not by interactions with the background plasma. A
scan in injection energy where injections are performed into the same plasma
conditions with different charging voltages would help in understanding this
issue, as would further study of the injection itself in a laboratory environment.
No attempt was made to compare the cross-field transport with experiment. Cross-field transport was included by setting the cross-field diffusion
to an empirical value of 1m2 s−1 . Disabling this transport had a significant
effect on the parallel transport but did not qualitatively alter the result.
Ideally the cross field transport would be set using cross-field transport coefficients obtained from the OSM solution, however the absence of drift terms
in OSM reduces the reliability of these coefficients.
No drift terms are included in the DIVIMP simulations, however the
effect of these terms on the parallel transport is likely to be dominated by
the energy of the injected particles. The effects of cross-field drifts seen in
previous work [51, 133] can potentially be seen, particularly in the case of
H-mode shot 29139 where a deviation from the magnetic field can be seen.
However uncertainties in both the magnetic equilibrium reconstruction and
the registration of the camera images mean that no firm conclusions can be
made from this.
The dominance of the energy of injected particles on the carbon transport
complicates the desire to understand the transport of impurities arising from
149
6.2 Further work
sputtering of the first wall and from impurity seeding, however the effect
of particle drifts can potentially be seen. The ability to vary the injected
energy also provide a way of studying the transport of high energy sputtered
products that may arise in the high power conditions expected in future
devices such as ITER.
6.2
Further work
The first and most obvious improvement to this work is the use of a more
tightly constrained EFIT equilibrium reconstruction. Although constrained
EFIT cases were run that improved the strike point location, problems with
generating grids suitable for use with DIVIMP-OSM-EIRENE meant that
this data was not used in the simulations presented here. Using this reconstruction would reduce the uncertainties in the background plasma solution
as well as more tightly constraining the injection location relative to the
strike points. With the present data it appears that the impurities may not
simply follow the field lines and actually deviate from the field, an effect that
may well be caused by particle drifts. However as the magnetic data is error
prone this may well be due to a combination of errors in the field used for
the projection onto the image and in the registration of the cameras used in
the projections.
Using an improved equilibrium may allow this effect to be studied with
the potential to include E × B drifts present in the SOL. Including the measured flow as a constraint in the background plasma solution would further
reduce uncertainties associated with the background plasma and allow a more
detailed study of the effect of each of the terms governing impurity transport.
To really gain the most from this data 3D image reconstruction could be
150
6.2 Further work
attempted for the shots where carbon II filters were used on both cameras.
Although full Abel inversion of the emission profile is likely to be problematic
due to there only being 2 viewing angles a reconstruction of the emission
surface should be possible. If this were to be done then comparisons could
then be made with modelling in 3D and again it may be possible to infer
information on drifts present in the SOL. Such 3D reconstructions could also
help understand the cross field turbulent transport that is the subject of
many current modelling efforts. Further to this the inclusion of drift effects
in DIVIMP would allow their impact on the injected plume to be better
studied.
The possibility to inject impurities into other regions of the plasma could
provide further data on edge impurity transport. The method also has the
potential to inject other conducting materials such as tungsten: this could
provide useful data for the latest devices that use tungsten as a plasma facing
material. However before this type of work is considered the difficulties
associated with this technique must be addressed, in particular the apparent
dominance of the energy of injected carbon on transport.
151
Bibliography
[1] S. A. Silburn, J. R. Harrison, J. Howard, K. J. Gibson, H. Meyer, C. A.
Michael, and R. M. Sharples. Coherence imaging of scrape-off-layer and
divertor impurity flows in the mega amp spherical tokamak. Review of
Scientific Instruments, 85:11D703, 2014.
[2] ITER Physics Basis Editors, ITER Physics Expert Group Chairs and
Co-Chairs and ITER Joint Central Team and Physics Integration Unit.
ITER Physics Basis. Nuclear Fusion, 39(12):2137–2627, 1999.
[3] R. J. Hayward et al. Design, construction and operation of the dite divertor field system (divertor injection tokamak experiment). In Symposium on Fusion Technology, 9th, Garmisch-Partenkirchen, West Germany, pages 157–162, June 1976.
[4] F. Wagner et al. Regime of improved confinement and high beta in
neutral-beam-heated divertor discharges of the ASDEX tokamak. Physical Review Letters, 49:1408–1412, 1982.
152
BIBLIOGRAPHY
[5] P. Stangeby. The Plasma Boundary of Magnetic Fusion Devices. Bristol: Institute of Physics Publishing, 2000.
[6] J. Wesson. Tokamaks. OUP, 2000.
[7]
[8] S. J. Zweben, B. D. Scott, J. L. Terry, B. LaBombard, J. W. Hughes,
and D. P. Stotler. Comparison of scrape-off layer turbulence in alcator c-mod with three dimensional gyrofluid computations. Physics of
Plasmas, 16:082505, 2009.
[9] D. K. Owens et al. Pdx divertor operation. Journal of Nuclear Materials, 93-94:213, 1980.
[10] C. S. Pitcher and P. C. Stangeby.
Experimental divertor physics.
Plasma Physics and Controlled Fusion, 39:779–930, 1997.
[11] D.N. Hill et al. Measurement and modeling of the DIII-D divertor
plasma. Journal of Nuclear Materials, 176-177:158–164, 1990.
[12] M. Keilhacker et al. Plasma boundary layer in limiter and divertor
tokamaks. Physica Scripta, T2/2:443–453, 1982.
[13] S. K. Erents et al A. V. Chankin, S. Clements. The effect of bt reversal
on the asymmetries between the strike zones in single null divertor
discharges: experiment and theories. Plasma Physics and Controlled
Fusion, 36:2853, 1994.
[14] I. H. Hutchinson et al. The effects of field reversal on the Alcator
C-Mod divertor. Plasma Physics and Controlled Fusion, 37(12):1389–
1406, 1995.
153
BIBLIOGRAPHY
[15] R Maingi et al. Effect of low density h-mode operation on edge and
divertor plasma parameters. Journal of Nuclear Materials, 220-222:
320–324, 1995.
[16] P. H. Rutherfod R. J. Goldston. Introduction to Plasma Physics. Institute of Physics Publishing Bristol and Philadelphia, 2003. ISBN 07503
0183 X.
[17] A. V. Chankin. Classical drifts in the tokamak sol and divertor: models
and experiment. Journal of Nuclear Materials, 241-243:199–213, 1997.
[18] S. I. Krasheninnikov. Reverse flow and parameter profiles in a dense
tokamak divertor plasma. Nuclear Fusion, 32:1927, 1992.
[19] J. A. Boedo et al. Flow reversal, convection, and modeling in the
DIII-D divertor. Physics of Plasmas, 5(12):4305–4310, 1998.
[20] N. Asakura et al. Measurement of natural plasma flow along the field
lines in the scrape-off layer on the jt-60u divertor tokamak. Physical
Review Letters, 84(14):3093–3096, 2000.
[21] G. F. Matthews S. K. Erents, A. V. Chankin and P. C. Stangeby.
Parallel flow in the JET scrape-off layer. Plasma Physics and Controlled
Fusion, 42:905–915, 2000.
[22] O. E. Garcia, R. A. Pitts, J. Horacek, J. Madsen, V. Naulin, A. H.
Nielsen, and J. Juul Rasmussen. Collisionality dependent transport in
tcv sol plasmas. Plasma Physics and Controlled Fusion, 49:B47–B57,
2007.
[23] B. A. Carreras. Plasma edge cross field transport: experiment and
theory. Journal of Nuclear Materials, 337-339:315–321, 2005.
154
BIBLIOGRAPHY
[24] A. Loarte. Understanding the edge physics of divertor experiments by
comparison of 2D edge code calculations and experimental measurements. Journal of Nuclear Materials, 241-243:118–134, 1997.
[25] A. Kendl and B. D. Scott. Flux-surface shaping effects on tokamak
edge turbulence and flows. Physics of Plasmas, 13:012504, 2006.
[26] V. Naulin. Shear flow generation and energetics in electromagnetic
turbulence. Physics of Plasmas, 12:052515, 2005.
[27] T. T. Ribeiro and B. D. Scott. Tokamak turbulence computations on
closed and open magnetic flux surfaces. Plasma Physics and Controlled
Fusion, 47:1657–1679, 2005.
[28] S.I. Krasheninnikov. On scrape off layer plasma transport. Physics
Letters A, 283:368–370, 2001.
[29] R. Jha et al. Intermittency in tokamak edge turbulence. Physical
Review Letters, 69(9):1375–1378, 1992.
[30] J. A. Boedo et al. Transport by intermittent convection in the boundary
of DIII-D. Physics of Plasmas, 8(11):4826–4833, 2001.
[31] V. Naulin. Turbulent transport and the plasma edge. Journal of Nuclear Materials, 363-365:24–31, 2007.
[32] J. A. Boedo et al. Intermittent convection in the boundary of DIII-D.
Journal of Nuclear Materials, 313-316:813–819, 2003.
[33] S. J. Zwebwn et al. Edge turbulence imaging in the Alcator C-Mod
tokamak. Physics of Plasmas, 9(5):1981–1989, 2002.
155
BIBLIOGRAPHY
[34] G. R. McKee et al. Experimental characterization of coherent, radiallysheared zonal flows in the DIII-D tokamak. Physics of Plasmas, 10(5):
1712–1719, 2003.
[35] P. W. Terry. Suppression of turbulence and transport by sheared flow.
Reviews of Modern Physics, 71(1):190–165, 2000.
[36] B. LaBombard et al. Transport-driven scrape-off layer flows and the xpoint dependence of the l-h power threshold in Alcator C-Mod. Physics
of Plasmas, 12:056111, 2005.
[37] R. A. Moyer et al. The role of turbulent transport in DIII-D edge and
divertor plasmas. Journal of Nuclear Materials, 241-243:633–638, 1997.
[38] R. F. Post. Impurity radiation losses from a high temperature plasma.
Journal of Nuclear Energy, Part C PLasma Physics, 3:273–286, 1961.
[39] Y Corre et al. Hybrid h-mode scenario with nitrogen seeding and
type III ELMs in JET. Plasma Physics and Controlled Fusion, 50(11):
115012, 2008.
[40] S. Brezinsek et al. Chemical erosion measurements in tokamaks by
spectroscopy. Physica Scripta, 111:42–48, 2004.
[41] L. Spitzer. Physics of fully ionized gases. Wiley, 1962.
[42] D. Reiter D. Reiser and M. Z. Tokar. Improved kinetic test particle
model for impurity transport in tokamaks. Nuclear Fusion, 38(2):165,
1998.
[43] W. Fundamenski S. K. Erents, R. A. Pitts, J. P. Gunn, and G. F.
Matthews. A comparison of experimental measurements and code re-
156
BIBLIOGRAPHY
sults to determine flows in the JET SOL. Plasma Physics and Controlled Fusion, 46:1757–1780, 2004.
[44] R. Scannell et al. Design of a new nd:yag thomson scattering system
for mast. Review of Scientific Instruments, 79(10):730, 2008.
[45] R. Pasqualotto et al. High resolution thomson scattering for Joint
European Torus (JET). Review of Scientific Instruments, 75(10):3891,
2004.
[46] J Howard, C Michael, F Glass, and A Danielsson. Time-resolved twodimensional plasma spectroscopy using coherence-imaging techniques.
Plasma Physics and Controlled Fusion, 45:1143–1166, 2003.
[47] J. Howard, A. Diallo, M. Creese, B. D. Blackwell, S. L. Allen, R. M.
Ellis, G. D. Porter, W. Meyer, M. E. Fenstermacher, N. H. Brooks,
M. E. Van Zeeland, and R. L. Boivin. Doppler coherence imaging
and tomography of flows in tokamak plasmas. Review of Scientific
Instruments, 81:10E528, 2010.
[48] M. A. Van Zeeland, J. H. Yu, N. H. Brooks, W. W. Heidbrink, K. H.
Burrell, R. J. Groebner, A. W. Hyatt, T. C. Luce, N. Pablant, W. M.
Solomon, and M. R. Wade. Active and passive spectroscopic imaging in
the diii-d tokamak. Plasma Physics and Controlled Fusion, 52:045006,
2010.
[49] S.J. Davies et al. Parallel electron temperature and density gradients
measured in the JET MkI divertor using thermal helium beams. Journal of Nuclear Materials, 241-243:426–432, 1997.
[50] Jablonksi et al. Local impurity puffing as a scrape-off layer diagnostic
157
BIBLIOGRAPHY
on the Alcator C-Mod tokamak. Journal of Nuclear Materials, 241-243:
782–787, 1997.
[51] S. Gangadhara and B. LaBombard. Impurity plume experiments in
the edge plasma of the Alcator C-mod tokamak. Plasma Physics and
Controlled Fusion, 46(10):1617–1646, 2004.
[52] L. Aho-Mantila, M. Wischmeier c, K. Krieger, V. Rohde, H.W. Mller,
D.P. Coster, M. Groth, A. Kirschner, R. Neu c, S. Potzel c, B. Sieglin,
E. Wolfrum, and The ASDEX Upgrade Team. Effect of e x b driven
transport on the deposition of carbon in the outer divertor of asdex
upgrade. Journal of Nuclear Materials, 415:S231–S234, 2011.
[53] G. M. McCracken et al. Screening of recycling and non-recycling impurities in the Alcator C-Mod tokamak. Journal of Nuclear Materials,
241-243:777–781, 1997.
[54] C.S. Pitcher et al. Carbon impurity transport around limiters in the
DITE tokamak. Journal of Nuclear Materials, 162-164:337–342, 1989.
[55] W. Horton and W. Rowan. Impurity transport studies in the texas
experimental tokamak (text). Physics of Plasmas, 1(4):901–908, 1994.
[56] A. G. McLean, J. W. Davis, P. C. Stangeby, N. H. Brooks, R. M. Ellis,
A. A. Haasz, D. L. Rudakov, W. P. West, D. G. Whyte, and C. P.
Wong. Porous plug gas injection systems for studies of hydrocarbon
dissociation and transport in the DIII-D tokamak. Review of Scientific
Instruments, 80(4):043501, 2009.
[57] K. Behringer. Measurement of ch4 /cd4 fluxes and of chemical carbon
erosion from ch/cd band emission. Journal of Nuclear Materials, 176177:606–610, 1990.
158
BIBLIOGRAPHY
[58] R. Pugno, K. Krieger, M. Airila, L. Aho-Mantila, A. Kreter, S. Brezinsek, V. Rohde, D. Coster, A. Chankin, M. Wischmeier, and the ASDEX
Upgrade Team. Investigation of local carbon transport in the asdex
upgrade divertor using 1 3ch4 puffing. Journal of Nuclear Materials,
390-391:68–71, 2009.
[59] J.D. Strachan et al. JET carbon screening experiments using methane
gas puffing and its relation to intrinsic carbon impurities. Nuclear
Fusion, 43:922–941, 2003.
[60] G.M. McCracken1990. A study of impurity transport in the plasma
boundary of textor using gas puffing. Journal of Nuclear Materials,
176-177:191–196, 1990.
[61] B. LaBombard et al. A novel tracer-gas injection system for scrape-off
layer impurity transport and screening experiments. Journal of Nuclear
Materials, 266-269:571–576, 1999.
[62] A. G. McLean, P. C. Stangeby, B. D. Bray, S. Brezinsek, N. H. Brooks,
J. W. Davis, R. C. Isler, A. Kirschner, R. Laengner, C. J. Lasnier,
Y. Mub, J. Munoz, D. L. Rudakov, O. Schmitz, E. A. Unterberg, J. G.
Watkins, D. G. Whyte, and C. P. C. Wong. Quantification of chemical erosion in the diii-d divertor and implications for iter. Journal of
Nuclear Materials, 415:S141–S144, 2011.
[63] A. Hakola, J. Likonen, L. Aho-Mantila, M. Groth1, S. Koivuranta,
K. Krieger, T. Kurki-Suonio, T. Makkonen, M. Mayer, H. W. Müller,
R. Neu, V. Rohde, and the ASDEX Upgrade Team. Migration and
deposition of 13c in the full-tungsten asdex upgrade tokamak. Plasma
Physics and Controlled Fusion, 52:065006, 2010.
159
BIBLIOGRAPHY
[64] R. Pugno, , K. Krieger, A. Kirschner, A. Kallenbach, D. P. Coster,
R. Dux, U. Fantz, J. Likonen, H. W. Muüller, J. Neuhauser, V. Rohde,
E. Vainonen-Ahlgren, and the ASDEX Upgrade Team. Carbon chemical erosion in H-mode discharges in ASDEX Upgrade divertor IIb:flux
dependence and local redeposition. Journal of Nuclear Materials, 337339:985–989, 2005.
[65] S. Brezinsek, A. Pospieszczyk, D. Borodin, M. F. Stamp, R. Pugno, ,
A. G. McLean, U. Fantz, A. Manhard, A. Kallenbach, N. H. Brooks,
M. Groth, Ph. Mertens, V. Philipps, U. Samm, DIII-D Teams the
TEXTOR, ASDEX Upgrade, and JET-EFDA Contributors. Hydrocarbon injection for quantification of chemical erosion yields in tokamaks.
Journal of Nuclear Materials, 363-365:1119–1128, 2007.
[66] P. C. Stangeby, A. G. McLean, J. D. Elder, N. H. Brooks, , W.P. West,
and D. Reiter. Measurements of the average energy of carbon atoms
released from breakup of methane in the main sol of diii-d compared
with divimp code modeling. Journal of Nuclear Materials, 363-365:
201–205, 2007.
[67] M.F. Stamp et al. Experimental determination of the contribution of
chemical sputtering of carbon on carbon core concentrations. Journal
of Nuclear Materials, 266-269:685, 1999.
[68] C. Giroud, R. Barnsley, P. Buratti, I. H. Coffey, M. von Hellermann,
C. Jupén, K. D. Lawson, A. Meigs, M. O’Mullane, A. D. Whiteford, KD. Zastrow, and the JET EFDA contributors. Method for experimental
determination of Z dependence of impurity transport on JET. Nuclear
Fusion, 47:313–330, 2007.
160
BIBLIOGRAPHY
[69] V. A. Soukhanovskii, H. W. Kugel, R. Kaita, R. Majeski, and A. L.
Roquemore. Supersonic gas injector for fueling and diagnostic applications on the national spherical torus experiment. Review of Scientific
Instruments, 75(10):4320, 2004.
[70] J.E. Menard, S. Gerhardt, M. Bell, J. Bialek, A. Brooks, J. Canik,
J. Chrzanowski, M. Denault, L. Dudek, D.A.Gates, N. Gorelenkov,
W. Guttenfelder, R. Hatcher, J. Hosea, R. Kaita, S. Kaye, C. Kessel,
E. Kolemen, H.Kugel, R. Maingi, M. Mardenfeld, D. Mueller, B. Nelson, C. Neumeyer, M. Ono, E. Perry, R. Ramakrishnan, R.Raman,
Y. Ren, S. Sabbagh, M. Smith, V. Soukhanovskii, T. Stevenson,
R. Strykowsky, D. Stutman, G. Taylor, P.Titus, K. Tresemer, K. Tritz,
M. Viola, M. Williams, R. Woolley, H. Yuh, H. Zhang, Y. Zhai,
A. Zolfaghari, and the NSTX Team. Overview of the physics and engineering design of nstx upgrade. Nuclear Fusion, 52(8):083015, 2012.
URL http://stacks.iop.org/0029-5515/52/i=8/a=083015.
[71] M.G. O’Mullane et al. Diagnostic exploitation of complex heavy elements in tokamak plasmas. Review of Scientific Instruments, 74(3):
2080–2083, 2003.
[72] D. Pasini et al. Measurements of impurity transport in JET. Plasma
Physics and Controlled Fusion, 34(5):677–685, 1992.
[73] Galli et al. Transient heat transport studies using laser ablated impurity injection in JET. Nuclear Fusion, 38(9):1355, 1998.
[74] R. Dux et al. Influence of the heating profile on impurity transport
in ASDEX Upgrade. Plasma Physics and Controlled Fusion, 45(45):
1815–1825, 2003.
161
BIBLIOGRAPHY
[75] R. Dux E. Scavino, J. S. Bakos and H. Weisen. Effects of plasma shape
on laser blow-off injected impurity transport in TCV. Plasma Physics
and Controlled Fusion, 45:1961–1974, 2003.
[76] A. Geier, K. Asmussen, A. Bard, R. Neu, and K. Krieger. A sublimation
probe for the injection of High-Z impurities into fusion devices. Review
of Scientific Instruments, 70(1):63–67, 1999.
[77] R. Schneider, X. Bonnin, K. Borrass, D. P. Coster, H. Kastelewicz,
D. Reiter, V. A. Rozhansky, , and B. J. Braams. Plasma edge physics
with b2-eirene. Contributions to Plasma Physics, 46(1-2):3–191, 2006.
[78] P. C. Stangeby, C. Farrell, S. Hoskins, and L. Wood. Monte carlo
modelling of impurity ion transport for a limiter source/sink. Nuclear
Fusion, 28(11):1945, 1988.
[79] M. Ali Mahdavi et al. Particle exhaust from plasma discharges with
an expanded-boundary divertor. Physical Review Letters, 47(22):1602–
1605, 1981.
[80] G. F. Counsell, J. W. Connor, S. K. Erents, A. R. Field, S. J. Fielding,
B. La Bombard, and K. M. Morel. Sol width scaling from consideration
of edge transport in tokamaks. Journal of Nuclear Materials, 266-269:
91–98, 1999.
[81] Farrokh Najmabadi Emad Zawaideh and Robert W. Conn. Generalized
fluid equations for parallel transport in collisional to weakly collisional
plasma. Physics of Fluids, 29(2):463, 1986.
[82] L. Tonks and I. Langmuir. A general theory of the plasma arc. Physical
Review, 34:876–922, 1929.
162
BIBLIOGRAPHY
[83] D. Reiter. Progress in two-dimensional plasma edge modelling. Journal
of Nuclear Materials, 196-198:80–89, 1992.
[84] P.C. Stangeby and J.D. Elder. Impurity retention by divertors part i:
One dimensional models. Nuclear Fusion, 35(11):1391–1412, 1995.
[85] B.J. Braams. Computational studies in tokamak equilibrium and transport. PhD thesis, University of Utrecht, 1986.
[86] A. Taroni, G. Corrigan, G. Radford, R. Simonini, J. Spence, and S. Weber. The multi-fluid codes edgeid and edge2d: Models and results.
Contributions to Plasma Physics, 32:438–443, 1992.
[87] R. Simonini, G. Corrigan, G. Radford, J. Spence, and A. Taroni. Models and numerics in the Multi-Fluid 2-D edge plasma code EDGE2D/U.
Contributions to Plasma Physics, 34:368–373, 1994.
[88] T. D. Rognlien, P. N. Brown, R. B. Campbell, T. B. Kaiser, D. A.
Knoll, P. R. McHugh, G. D. Porter, M. E. Rensink, and G. R. Smith.
2-d fluid transport simulations of gaseous/radiative divertors. Contributions to Plasma Physics, 34:362–367, 1994.
[89] T.D. Rognlien et al. Advances in understanding tokamak edge/scrapeoff layer transport. In 23rd IAEA Fusion Energy Conference, 11-16
October 2010, Daejeon, Republic of Korea, pages P3–05, October 2010.
[90] P. Börne D. Reiter, M. Baelmans. The eirene and b2-eirene codes.
Fusion Science and Technology, 47(2):172–186, 2005.
[91] A. V. Chankin, D. P. Coster, R. Dux, Ch. Fuchs, G. Haas, A. Herrmann, L. D. Horton, A. Kallenbach, M. Kaufmann, Ch. Konz,
163
BIBLIOGRAPHY
K. Lackner, C. Maggi, H. W. Müller, J. Neuhauser, R. Pugno, M. Reich, and W. Schneider. SOLPS modelling of ASDEX upgrade H-mode
plasma. Plasma Physics and Controlled Fusion, 48:839–868, 2006.
[92] Y. Chen, G. Xu, J. Hu, and D. P. Coster. Edge plasma modelling
for HT-7 superconducting tokamak experiments. Journal of Nuclear
Materials, 363-365:54–549, 2007.
[93] E. Havlı́čková, M. Wischmeier, and G. Fishpool. Modelling the effect
of the super-x divertor in mast upgrade on transition to detachment
and distribution of volumetric power losses. Contributions to Plasma
Physics, 54(4-6):448–453, 2014.
[94] L. W. Owen, J. M. Canik, R. J. Groebner, J. D. Callen, X. Bonnin, and
T. H. Osborne. Comparing 1.5D ONETWO and 2D SOLPS analyses
of inter-ELM H-mode plasma in DIII-D. Nuclear Fusion, 50(6):064017,
2010.
[95] P. C. Stangeby, J. M. Canik, and D. G. Whyte. The relation between upstream density and temperature widths in the scrape-off layer
and the power width in an attached divertor. Nuclear Fusion, 50(12):
125003, 2010.
[96] L. Aho-Mantila, M. Wischmeier, H. W. Müller, D. P. Coster S. Potzel,
X. Bonnin, G. D. Conway, and the ASDEX Upgrade Team. Outer
divertor of asdex upgrade in low-density l-mode discharges in forward
and reversed magnetic field: I. comparison between measured plasma
conditions and solps5.0 code calculations. Nuclear Fusion, 52:103006,
2012.
164
BIBLIOGRAPHY
[97] M. Wischmeier, M. Groth, A. Kallenbach, A. V. Chankin, D. P. Coster,
R. Dux, A. Herrmann, H. W. Müller, R. Pugno, D. Reiter, A. Scarabosio, J. G. Watkins, DIII-D team, and ASDEX Upgrade team. Current
understanding of divertor detachment: Experiments and modelling.
Journal of Nuclear Materials, 390-391:250–254, 2009.
[98] B. Viola, G. Calabró, F. Crisanti, G. Maddaluno, V. Pericoli Ridolfini,
R. Albanese, G. Artaserse, R. Zag/’orski, A. Kallenbach, W. Treutterer, and ASDEX Upgrade Team. Divertor plasma shaping and modeling of ASDEX upgrade. page P5.069, 2011.
[99] S. K. Erents, W. Fundamenski, G. Corrigan, G. F. Matthews,
R. Zagorski, and EFDA-JET Contributors. EDGE2D modelling of
JET and ITER including the combined effect of guiding centre drifts
and an edge transport barrier. Journal of Nuclear Materials, 363-367:
565–569, 2007.
[100] B. Viola, G. Corrigan, D. Harting, G. Maddaluno, M. Mattia, V. Pericoli Ridolfini, and R. Zagórski. Preliminary comparison of the conventional and quasi-snowflake divertor configurations with the 2d code
edge2d/eirene in the fast tokamak. Contributions to Plasma Physics,
54:459–463, 2014.
[101] A. Kallenbach, Y. Andrew, M. Beurskens, G. Corrigan, T. Eich,
S. Jachmich, M. Kempenaars, A. Korotkov, A. Loarte, G. Matthew,
P. Monier-Garbet, G. Saibene, J. Spence, W. Suttrop, and JET EFDA
Contributors. EDGE2D modelling of edge profiles obtained in jet diagnostic optimized configuration. Plasma Physics and Controlled Fusion,
46:431, 2004.
165
BIBLIOGRAPHY
[102] J. D. Strachan, J. Likonen, P. Coad, M. Rubel, A. Widdowson, M. Airila, P. Andrew, S. Brezinsek, G. Corrigan, H. G. Esser, S. Jachmich,
A. Kallenbach, A. Kirschner, A. Kreter, G. F. Matthews, V. Philipps,
R. A. Pitts, J. Spence, M. Stamp, S. Wiesen, and JET-EFDA contributors. Modelling of carbon migration during JET
13
C injection
experiments. Nuclear Fusion, 48:105002, 2008.
[103] C. Guillemaut, R. A. Pitts, A. S. Kukushkin, J. P. Gunn, J. Bucalossi,
G. Arnoux, P. Belo, S. Brezinsek, M. Brix, G. Corrigan, S. Devaux,
J. Flanagan, M. Groth, D. Harting, A. Huber, S. Jachmich, U. Kruezi,
M. Lehnen, C. Marchetto, S. Marse, A. G. Meigs, O. Meyer, M. Stamp,
J. D. Strachan, S. Wiesen, M. Wischmeier, and JET EFDA Contributors. Influence of atomic physics on EDGE2D-EIRENE simulations of
jet divertor detachment with carbon and beryllium/tungsten plasmafacing components. Nuclear Fusion, 54:093012, 2014.
[104] G. S. Kirnev, G. Corrigan, D. Coster, S. K. Erents, W. Fundamenski,
G. F. Matthews, and R. A. Pitts. Edge2d code simulations of sol flows
and inout divertor asymmetries in jet. Journal of Nuclear Materials,
337-339:271–275, 2005.
[105] .P. Coster, , X. Bonnin, G. Corrigan, G. S. Kirnev, G. Matthews,
J. Spence, and Contributors to the EFDA-JET work programme.
Benchmarking tokamak edge modelling codes. Journal of Nuclear Materials, 337-339:366–370, 2005.
[106] S.L. Allen, J. A. Boedo, A. S. Bozek, N. H. Brooks, T. N. Carlstrom,
T. A. Casper, R. J. Colchin, T. E. Evans, M. E. Fenstermacher, M. E.
Friend, R. C. Islera, R. Jayakumar, C. J. Lasnier, A. W. Leonard, M. A.
Mahdavi, R. Maingi, G. R. McKee, R. A. Moyer, M. Murakami, T. H.
166
BIBLIOGRAPHY
Osborne, R. C. O’Neill, T. W. Petrie, G. D. Porter, A. T. Ramsey,
M. J. Schaffer, P. C. Stangeby, R. D. Stambaugh, M. R. Wade, J. G.
Watking, W. P. West, D. G. Whyte, and N. S. Wolf. Experiments and
computational modeling focused on divertor and sol optimization for
advanced tokamak operation on DIII-D. Journal of Nuclear Materials,
290-293:995–1001, 2001.
[107] J.M. Munoz Burgos, A. W. Leonard, S. D. Loch, and C. P. Ballance.
Evaluation of an improved atomic data basis for carbon in uedge emission modeling for l-mode plasmas in diii-d. Journal of Nuclear Materials, 438:S406–S409, 2013.
[108] T. W. Petrie, N. H. Brooks, M. E. Fenstermacher, M. Groth, A. W.
Hyatt, C. J. Lasnier, A. W. Leonard, G. D. Porter, M. J. Schaffer,
M. R. Wade, J. G. Watkins, and W. P. West. Sensitivity of injected
argon behavior to changes in magnetic balance in double-null plasmas
in diii-d. Journal of Nuclear Materials, 390-391:242–245, 2009.
[109] A. Yu. Pigarov, S. I. Krasheninnikov, T. D. Rognlien, C. J. Lasnier,
and E. Unterberg. Dynamic plasma-wall modeling of elmy h-mode with
uedge-mb-w. Journal of Nuclear Materials, 463:705–708, 2015.
[110] G. D. Porter, T. W. Petrie, T. D. Rognlien, and M. E. Rensink.
UEDGE simulation of edge plasmas in DIII-D double null configurations. Physics of Plasmas, 17:112501, 2010.
[111] W. P. West, G. D. Porter, T. E. Evans, P. Stangeby, N. H. Brooks,
M. E. Fenstermacher, R. C. Isler, T. D. Rognlien, M. R. Wade, D. G.
Whyte, and N. S. Wolf. Modeling of carbon transport in the divertor
167
BIBLIOGRAPHY
and SOL of DIII-D during high performance plasma operation. Journal
of Nuclear Materials, 290-293:783–787, 2001.
[112] M. Groth, G. D. Porter, M. E. Rensink, T. D. Rognlien, S. Wiesen,
M. Wischmeier, T. Eich, A. Herrmann, S. Jachmich, C. J. Lasnier,
H. W. Müller, J. G. Watkins, M. N. A. Beurskens, B. D. Bray,
S. Brezinsek, N. H. Brooks, M. E. Fenstermacher, C. Fuchs, A. Huber, A. Kallenbach, A. W. Leonard, A. Meigs, D. L. Rudakov, ASDEX
Upgrade Teams The DIII-D, and JET EFDA Contributors. Influence
of cross-field drifts and chemical sputtering on simulations of divertor
particle and heat loads in ohmic and l-mode plasmas in diii-d, aug, and
jet using uedge. Journal of Nuclear Materials, 415:S530–S534, 2011.
[113] E. T. Meier, V. A. Soukhanovskii, R. E. Bell, A. Diallo, R. Kaita, B. P.
LeBlanc, A. G. McLean, M. Podestà, and F. Scott T.D. Rognlien and.
Modeling detachment physics in the nstx snowflake divertor. Journal
of Nuclear Materials, 463:1200–1204, 2015.
[114] T. D. Rognlien, R. H. Bulmer, M. E. Rensink, and J. N. Brooks. Scrapeoff layer plasmas for iter with 2nd x-point and convective transport
effects. Journal of Nuclear Materials, 363-365:658–663, 2007.
[115] S.K. Erents and P.C. Stangeby. Heat transport in the JET scrape-off
layer. Nuclear Fusion, 38:1637, 1998.
[116] P.C. Stangeby W. Fundamenski and J.D. Elder. A cfd onion-skin model
for the interpretation of edge experiments. Journal of Nuclear Materials, 266-269:1045–1050, 1999.
[117] S. Lisgo et al. OSM-EIRENE modeling of neutral pressures in the
168
BIBLIOGRAPHY
Alcator C-Mod divertor. Journal of Nuclear Materials, 337-339:139–
145, 2005.
[118] W. Fundamenski, S.K. Erents, G.F. Matthews, A.V. Chankin, V. Riccardo, P.C. Stangeby, and J.D. Elder. Analysis of SOL behaviour in
JET MkIIGB using an advanced onion-skin solver (OSM2). jnuclmater,
290-293:593, 2001.
[119] J. Harrison, S. Lisgo, G. F. Counsell, K. Gibson, J. Dowling, L. Trojan,
and D. Reiter. Interpretive modelling of scrape-off plasmas on the mast
tokamak. Journal of Nuclear Materials, 390-391:392–394, 2009.
[120] A. Kirk, W. Fundamenski, J-W. Ahn, and G. Counsell. Parallel SOL
transport in MAST and JET: the impact of the mirror force. Plasma
Physics and Controlled Fusion, 45:1445–1463, 2003.
[121] D. Harting et al. 3D Edge Transport Studies with EMC3-EIRENE for
the Dynamic Ergodic Divertor (DED) at TEXTOR. Contributions to
Plasma Physics, 48(1-3):99–105, 2008.
[122] M. Kobayashi et al. 3D edge transport analysis of ITER start-up configuration for limiter power load assessment. Nuclear Fusion, 47(2):
61–73, 2007.
[123] B. D. Dudson, A. Allen, G. Breyiannis, E. Brugger, J. Buchanan,
L. Easy, S. Farley, I. Joseph, M. Kim, A. D. McGann, J. T. Omotani,
M. V. Umansky, N. R. Walkden, T. Xia, and X. Q. Xu. Bout++:
Recent and current developments. Journal of Plasma Physics, 81:
365810104, 2014.
[124] S. Ku et al. Gyrokinetic particle simulation of neoclassical transport in
169
BIBLIOGRAPHY
the pedestal/scrape-off region of a tokamak plasma. Journal of Physics:
Conference Series, 46:87–91, 2006.
[125] K. Bodi R.H. Cohen X.Q. Xu1, S. Krasheninnikov, and T.D. Rognlien.
Tempest simulations of the plasma transport in a single-null tokamak
geometry. Nuclear Fusion, 50:064003, 2010.
[126] F. Jenko and W. Dorland. Nonlinear electromagnetic gyrokinetic simulations of tokamak plasmas. Plasma Physics and Controlled Fusion,
43:A141–A150, 2001.
[127] M. Kotschenreuther W. Dorland, F. Jenko and B. N. Rogers. Electron
temperature gradient turbulence. Physical Review Letters, 85:5579–
5582, 2000.
[128] Y. Chen and S. E. Parker. Electromagnetic gyrokinetic f particle-in-cell
turbulence simulation with realistic equilibrium profiles and geometry.
Journal of Computational Physics, 220:839–855, 2007.
[129] R.H. Cohen et al. Testing and plans for the cogent edge kinetic code,
2010.
[130] J. Cummings et al. Plasma Edge Kinetic-MHD Modeling in Tokamaks
Using KeplerWorkflow for Code Coupling, Data Management and Visualization. Communications in Computational Physics, 4(3):675–702,
2008.
[131] J. Winterb A. Kirschnera, V. Philippsa and U. Köglera. Simulation of
the plasma-wall interaction in a tokamak with the monte carlo code
ero-textor. Nuclear Fusion, 40:989, 2000.
170
BIBLIOGRAPHY
[132] K. Shimizu, H. Kubo, T. Takizuka, M. Azumi, M. Shimada, S. Tsuji,
N. Hosogane, T. Sugie, A. Sakasai, N. Asakura, and S. Higashijim. Impurity transport modelling and simulation analysis of impurity behavior in JT-60U. Journal of Nuclear Materials, 220-222:410–414, 1995.
[133] L. Aho-Mantila, M. Wischmeier, K. Krieger, V. Rohde, A. Hakola,
S. Potzel, A. Kirschner, and D. Borodin the ASDEX Upgrade Team.
Outer divertor of asdex upgrade in low-density l-mode discharges in
forward and reversed magnetic field: Ii. analysis of local impurity migration. Nuclear Fusion, 52:103007, 2012.
[134] T. Makkonen, M. Groth, T. Kurki-Suonio, K. Krieger, L. Aho-Mantila,
A. Hakola, J. Likonen, H. W. Müller, and the ASDEX Upgrade Team.
Divimp simulations of 13c puffing experiments in asdex upgrade l-mode
plasma. Journal of Nuclear Materials, 415:S479–S482, 2011.
[135] K. Ohya, K. Inai, T. Tanabe, and H. Takenaga. Modeling of asymmetric redeposition distribution between inner and outer regions of the
w-shaped divertor in jt-60u. Journal of Nuclear Materials, 363-365:
78–85, 2007.
[136] D. Naujoks, R. Behrisch, J. P. Coad, and L. C. J. M. De Kock. Carbon
chemical erosion in H-mode discharges in ASDEX Upgrade divertor
IIb:flux dependence and local redeposition. Journal of Nuclear Materials, 337-339:985–989, 2005.
[137] H. Kawashima, K. Shimizu, and T. Takizuka. Development of integrated sol/divertor code and simulation study of the jt-60u/jt-60sa
tokamaks. Plasma Physics and Controlled Fusion, 49:S77–S85, 2007.
171
BIBLIOGRAPHY
[138] K. Shimizu, T. Takizuka, S. Sakurai, H. Tamai, H. Takenaga, H. Kubo,
and Y. Miura. Simulation of divertor detachment characteristics in jt60 with superconducting coils. Journal of Nuclear Materials, 313-316:
1277–1281, 2003.
[139] K. Shimizu, T. Takizuka, K. Ohya, K. Inai, T. Nakano, A. Takayama,
H. Kawashima, and K. Hoshino. Kinetic modelling of impurity transport in detached plasma for integrated divertor simulation with SONIC
(SOLDOR/NEUT2D/IMPMC/EDDY). Nuclear Fusion, 49:065028,
2009.
[140] K. Hoshino, , K. Shimizu, T. Takizuka, N. Asakura, and T. Nakano.
Improvement of the detachment modelling in the SONIC simulation.
Journal of Nuclear Materials, 415:S549–S552, 2011.
[141] H. Kawashima, K. Hoshino, K. Shimizu, T. Takizuka, S. Ide, S. Sakurai, and N. Asakura. Evaluation of heat and particle controllability
on the jt-60sa divertor. Journal of Nuclear Materials, 415:S948–S951,
2011.
[142] K. Shimizu, T. Takizuka, and H. Kawashima. Kinetic effect of thermal
force on impurity transport: Simulation of JT-60SA divertor with integrated divertor code SONIC. Journal of Nuclear Materials, 49:065028,
2009.
[143] S. Ishida, P. Barabaschi, Y. Kamada, and the JT-60SA Team. Status
and prospect of the JT-60SA project. Fusion Engineering and Design,
85:2070–2079, 2010.
[144] A. G. McLean, J. D. Elder, P. C. Stangeby, S. L. Allen, J. A. Boedo,
N. H. Brooks, M. E. Fenstermacher, M. Groth, S. Lisgoand A. Nagy,
172
BIBLIOGRAPHY
D. L. Rudakov, W. R. Wampler, J. G. Watkins, W. P. West, and D. G.
Whyte. Divimp modeling of the toroidally symmetrical injection of
13ch4 into the upper sol of diii-d. Journal of Nuclear Materials, 337339:124–128, 2005.
[145] Y. Mu, J. D. Elder, P. C. Stangeby, and A. G. McLean.
3D-
DIVIMP(HC) code modeling of DIII-D DiMES porous plug injector
experiments. Journal of Nuclear Materials, 415:S145–S148, 2011.
[146] A. Järvinen, C. Giroud, M. Groth, K. Krieger, D. Moulton, S. Wiesen,
S. Brezinsek, and JET-EFDA contributors. Divimp simulation of W
transport in the SOL of JET H-mode plasmas. T145:014013, 2011.
[147] A. Xuereb, M. Groth, K. Krieger, , O. Asunta, T. Kurki-Suonio,
J. Likonen, D. P. Coster, and the ASDEX Upgrade Team. DIVIMP-B2EIRENE modelling of 13 c migration and deposition in ASDEX Upgrade
L-mode plasmas. Journal of Nuclear Materials, 396:228–233, 2010.
[148] K. Schmid, K. Krieger, A. Kukushkin, and A. Loarte. DIVIMP modeling of tungsten impurity transport in ITER. Journal of Nuclear Materials, 363-365:674–679, 2007.
[149] M. Cox. The mega ampere spherical tokamak. Fusion Engineering and
Design, 46:397–404, 1999.
[150] G. de Temmerman, M. Bacharis, J. Dowling, and S. Lisgo. Dust creation and transport in mast. Nuclear Fusion, 50:105012, 2010.
[151] S. Elmore, S. Y. Allan, A. Kirk, G. Fishpool, J. Harrison, P. Tamain,
M. Kočan, R. Gaffka, R. Stephen, J. W. Bradley, and the MAST Team.
173
BIBLIOGRAPHY
Upstream and divertor ion temperature measurements on mast by retarding field energy analyser. Plasma Physics and Controlled Fusion,
54:065001, 2012.
[152] V. Rozhansky, P. Molchanov, S. Voskoboynikov, G. Counsell, A. Kirk,
D. Coster, and R. Schneider. Modeling of the parametric dependence
of the edge toroidal rotation for mast and asdex upgrade. Journal of
Nuclear Materials, 363-365:664–668, 2007.
[153] J. Marshall. Performance of a hydromagnetic plasma gun. Physics of
Fluids, 3:134–135, 1960.
[154] John F O’Hanlon. A User’s Guide to Vacuum Technology. Wiley, 2003.
[155] Günter Sauerbrey.
Verwendung von schwingquarzen zur wägung
dünner schichten und zur mikrowägung. Zeitschrift für Physik, 155
(2):206–222, 1959.
[156] C.P.C. Wong et al. Divertor materials evaluation system (dimes). Journal of Nuclear Materials, 258-263:433–439, 1998.
[157] S.J.Fielding G.F. Counsell, J-W. Ahna and G.P.Maddison. Divertor
power loading studies in the mast tokamak. In 27th EPS Conference
on Contr. Fusion and Plasma Phys. Budapest, Hungary, volume 24B,
pages 1577–1580, 2000.
[158] K. J. Gibson et al. New physics capabilities from the upgraded thomson
scattering diagnostic on mast. Plasma Physics and Controlled Fusion,
52:124041, 2010.
[159] R. Scannell et al. A 130 point nd:yag thomson scattering diagnostic on
mast. Review of Scientific Instruments, 81:10D520, 2010.
174
BIBLIOGRAPHY
[160] L.L. Lao, H. St. John, R.D. Stambaugh, A.G. Kellman, and W. Pfeiffer. Reconstruction of current profile parameters and plasma shapes in
tokamaks. Nuclear Fusion, 25:1611, 1985.
[161] J. D. Elder. Divimp options. http://starfire.utias.utoronto.ca/
divimp/docs/divdocs.html.
[162] S. Lisgo, P. C. Stangeby, J. D. Elder, J. A. Boedo, B. D. Bray, N. H.
Brooks, M. E. Fenstermacher, M. Groth, D. Reiter, D. L. Rudakov,
J. G. Watkins, W. P. West, and D. G. Whyte. Re-construction of
detached divertor plasma conditions in DIII-D using spectroscopic and
probe data. Journal of Nuclear Materials, 337-339:256–260, 2005.
[163] H.
P.
Summers.
The ADAS User Manual,
version 2.6
http://www.adas.ac.uk. 2004.
[164] A. J. Wootton, B. A. Carreras, H. Matsumoto, W. A. Peebles, Ch. P.
Ritz, and P. W. Terry amd S. J. Zweben. Fluctuations and anonymous
transport in tokamaks. Phys. Fluids B, 2(12):2879–2903, 1990.
[165] A. Anders, S. Anders, I. G. Brown, M. R. Dickinson, and R. A. MacGill.
Metal plasma immersion ion implantation and deposition using vacuum
arc plasma sources. Journal of Vacuum Science and Technology, 12:
815, 1994.
[166] J. Rosén, J. M. Schneider, and A Anders. Charge state dependence
of cathodic vacuum arc ion energy and velocity distributions. Applied
Physics Letters, 89:141502, 2006.
[167] A. G. Nikolaev, E. M. Oks, G. Yu. Yushkov K. P. Savkin, and I. G.
Brown. Upgraded vacuum arc ion source for metal ion implantation.
Review of Scientific Instruments, 83:02A501, 2012.
175
BIBLIOGRAPHY
[168] E. Byon and A. Anders. Ion energy distribution functions of vacuum
arc plasmas. Journal of Applied Physics, 93(4):1899, 2003.
[169] K. Hoshino, A. Hatayama, N. Asakura, H. Kawashima, R. Schneider,
and D. Coster. Numerical analysis of the SOL/divertor plasma flow
with the effect of drifts. Journal of Nuclear Materials, 363-365:539–
543, 2007.
[170] L. Aho-Mantila, M. Wischmeier, M. I. Airila, A. V. Chankin, D.P.
Coster Ch. Fuchs, M. Groth, A. Kirschner, K. Krieger, H. W. Müller,
E. Wolfrum, and the ASDEX Upgrade Team. Modelling of carbon
transport in the outer divertor plasma of asdex upgrade. Contributions
to Plasma Physics, 50(3-5):439–444, 2010.
[171] G. D. Porter, T. D. Rognlien, M. E. Rensink, A. Loarte, N. Asakura,
H. Takenaga, G. Matthews, and Contributors to the EFDA-JET
Work Programme. Simulation of the effect of plasma flows in DIII-D,
JET, and JT-60U. Journal of Nuclear Materials, 313-316:1085–1088,
2003.
[172] R. Ding, A. Kirschner, M. Z. Tokar, M. Koltunov, D. Borodin,
S. Brezinsek, A. Kreter, J. L. Chen, J. G. Li, and G.-N. Luo. Studies of the influence of external hydrocarbon injection on local plasma
conditions and resulting carbon transport. 415:S270–S273, 2011.
176
Appendices
177
APPENDIX
A
Manufacturing drawings of the injector head
178
APPENDIX
B
Electrical schematics of the MAST installation
194
APPENDIX
C
Commissioning and initial experiments
C.1
Commissioning and in-situ testing
The injector head was first installed on MAST on Friday 23rd September
2011. Testing of the power supply was started on Wednesday 28th (shot
26851) using a 300Ω dummy load without any connection to the injector
head. The testing was performed during a session dedicated to other work
so the spark trigger was set to 400ms, significantly after the main time of
interest for the primary experiment. During this testing the capacitor bank
would discharge roughly 100ms into the MAST pulse, before this time the
capacitors would trigger normally, after this time no triggering was possible.
No signal was observed from the current monitor during or after the voltage
drop. Testing continued on Friday 30th September and the cause of the
discharge was identified as the IPS box lid interlock. The magnetic relay
200
C.2 First experimental sessions - Oct 2011
used in the interlock was deactivating and returning to a closed state due to
the magnetic field underneath the MAST vessel. This caused the capacitors
to discharge and prevented further charging. The MAST safety officer agreed
that as long as the box was in-situ it would be safe to disable this interlock,
provided that it was re-enabled once the IPS box was removed. Disabling
the interlock solved this problem and the power supply was shown to work
as expected.
The injector head was connected to the power supplies on 4th October.
Although the power supplies were now known to be working and the optical
trigger was being received no discharge was observed. This problem was
traced to an incorrectly assembled cable and fixed the same day. The first
successful firing of the injector was during pulse 26998 on Wednesday 5th
October.
Before injection into plasma a series of discharges at increasing voltage
up to the maximum of 2.5kV were attempted into vacuum conditions. Only
very small current readings were seen by the current probe and no effect was
seen on any of the MAST systems. This was not unexpected as the plasma
was expected to play a significant role in the breakdown. The fact that no
breakdown occurred also made it unlikely that any external systems could
have been affected. It was decided that test pulses into plasma shots would
be required to properly test the system.
C.2
First experimental sessions - Oct 2011
Ohmic L-mode plasmas were chosen for the commissioning and initial experimental sessions. The uncertainty associated with ELMs occurring during
H-mode plasma increases the complexity of both data processing and mod-
201
C.2 First experimental sessions - Oct 2011
elling. It was also uncertain how the injector systems would react to high
power plasmas as the injector power supplies are directly coupled to the
plasma through the injector head. A relatively benign plasma would therefore be safer. Not relying on neutral beams (NBI) also removes a potential
problem when running experiments.
The fixed location of the DSF and the sweeping of the MAST strike points
mean that only a limited number of MAST plasma configurations are suitable
for study with diagnostics on the DSF. In the large majority of pulses the
strike point crosses the DSF before the current flat top is reached. Previous
studies using a retarding field energy analyser fitted to the DSF[151] have
developed several shots that cross the DSF at a suitable time during the
shot. One of these shots, 26776, was chosen as a likely candidate for use in
the carbon injection experiments. This is a low current (400kA) Ohmically
heated shot. The MAST standard shot was also used for these experiments
due to its simplicity and reliability.
C.2.1
Wednesday 5th October 2011
For the first full session on Wednesday 5th October it was decided to use the
MAST standard shot as this was believed to be the most fail-safe approach.
Unfortunately an undocumented change to the gas control system caused
problems running the standard shot and the session had to be abandoned
without any useful data being recorded.
C.2.2
Friday 7th October 2011
During the following session on Friday 7th October the injector failed to
discharge. This was due to a failure of the IGBT trigger in the power supplies,
202
C.2 First experimental sessions - Oct 2011
see section 2.4.3. Area entry was required to remove the power supplies and
the IGBT was then replaced before the supplies were reinstalled.
C.2.3
Friday 14th October 2011
The first camera data was taken on Friday 14th June. The majority of these
shots used MAST pulse 26776 as a reference. The spark location was varied
from ≈ 4cm inboard of the outer strike point to ≈ 3cm outboard of the outer
strike point. Both cameras were operated at a speed of 75kHz. A total of 17
successful shots were run in this session with shot numbers 27074 to 27090.
C.2.4
Monday 17th October 2011
A follow up session was then conducted using the MAST standard shot which
operates at a higher current (770kA) than the previous shots. Although
there was excessive noise on some of these shots the image data taken was
still potentially useful. A total of 10 successful shots were run in this session
with shot numbers 27095 to 27103.
203